I'm not a professional Varian player. I'm not a professional anything player, actually, but Varian is in my top five favourite heroes, so I play him a lot, and if I was a professional anything player, I'd be a professional Varian player.
When I say I'm not a professional, I mean I have never, not once, ever, in my whole life, played a ranked game, and very rarely do I do unranked.
Without further ado, let's dive in to the guide itself. All feedback is welcome and appreciated!

EDIT: As of now, I have played ranked (eight games, to date), but only a couple, and not all of them as Varian. I got MVP on my first game on him though, so that's cool :)

PROS

-High survivability
-High aggression

CONS

-Eats up mana at low levels
-If you fail your ability order it could get you killed

Varian used to be a multiclass hero, before the roles' switch. He could either be an assassin or a warrior (now called tank). In my mind, he's still a multiclass hero, but instead of two options, he has three: Tank (with Taunt); Bruiser (with Twin Blades of Fury); or Melee Assassin (with Colossus Smash).
He's probably my favourite hero, with Murky coming in as a close second. He can deal damage, setup for his allies, and hold his ground--no matter what build you go with, although based on your heroic choice you will capitalize on one of these strengths.

PROS

-Incredible burst damage

CONS

-Low HP
-Easily ganked

This is my standard build, good in most situations. Especially good against squishy heroes, but be wary of your HP. The C-Smash build is easily ganked, and has a small health pool, but these two negative factors do not together take away from the sheer glory of shredding Tracer in 5 seconds. Unfortunately, because I don't often get in with a tank and a bruiser, I often can't play this.
Against heroes like Diablo you can still be useful, however. Typically, if the enemy team has a lot of high-health heroes (or tanky ones in general), Twin Blades is better than this one, because of the sustained damage. That being said, when paired with Li-Ming or a similar very high damage potential hero, hitting Colossus Smash on anyone will allow for intense damage. Consider the following example, by way of illustration. The first number is the flat damage, the second is the C-Smashed damage.

Varian BA: 74/98.8
Varian BA w/ Colossus Smash: 148/177.6
Varian BA w/ High King's Quest: 134/160.8
Varian BA w/ High King's Quest & Colossus Smash: 268/321.6
Butcher BA w/ Full Fresh Meat: 335/402

As you can see, popping your heroic can mean a huge difference in a team fight, and getting Master at Arms at level 20 can mean you apply that whopping damage increase against multiple enemies. An ally proceeding to use an AoE damage (whether Tracer's Pulse Bomb or Kael'thas's Phoenix.
Because this bonus applies not only to you, travelling with an ally can boost your chance of small-scale battle success from low to very high.

This build is a good choice if the following are true:

You have a tank and a bruiser.
They have a lot of low-health heroes.

This build is a bad choice if the following are true:

You lack a tank, or at least two bruisers.
You don't have high-damage allies, or if they don't have low-health heroes.

PROS

-Powerful sustain damage
-Reliable self-sustain
-Can be a tank in periods of necessity

CONS

-Very low burst potential

An awesome build, high self-sustain and sustained damage, excellent point control and can solo boss at later levels. To illustrate the full awesomeness of this build, let's take a quick look at damage/second, which I will cover in depth later in the ability section:

Level One BA: 74
Level One BA w/ TBoF: 55.5.
Level One AS: 1.25/second
Level One AS w/ TBoF: 2.5/second
Level One Damage/Second: 92.5
Level One Damage/Second w/ TBoF: 138.75

You can see where this is going. Massive increase to damage with Twin Blades of Fury, and the best thing is it isn't active, which means it's a total damage increase, not something you need to time or think about the pros/cons of saving for later. This build can actually function as a kind of tank, especially when paired with Lt. Morales's Stim Drone. Let's take a look at what that could do to you. We won't look at the first of each pair of numbers, only the TBoF damage, from earlier, at level one. We're taking into account Second Wind, your level seven healing talent, which heals you for 1% of your max health per attack:

Without Stim Drone:
Damage/Second: 138.75
Attacks/Second: 2.5
Healing/Second: 2.5% of max
Movement Bonus after Attacking: 30%

With Stim Drone:
Damage/Second: 242.8125
Attacks/Second: 4.375
Healing/Second: 4.375% of max
Movement Bonus after Attacking: 55%

You read that right--team up with Lt. Morales and you can slam off 4.375 attacks per second, which rounds to 4.4 attacks per second, allowing you to heal roughly 4.4% every second. Also, no one can get away from you. This is a powerful synergy that you should not pass up if you have someone willing to play Lt. Morales!

In general, this build can be far more aggressive than the other two simply because you are far more self-sustainable. You can cut through minion waves fairly quickly, as well as towers, so split-pushing is a good option.

One last note: Abathur's level 4 talent Adrenal Overload increases Symbiote host's attack speed by 25%. This is a sustainable speed increase, not a one-and-gone thing like Stim Drone, so is incredibly powerful. Moreover, Soma Transference can provide you with increased regen when surrounded.

PROS

-High health
-Can pull enemies off allies

CONS

-Low damage

An underrated build, in my opinion, can save squishy casters as well as pull enemies into ally effects such as Pyroblast. One fun thing to do is go with this build while you have another tank already, as it can allow you to make some nasty setups. Pairing with Blaze can be fun, as well as any other high-CC tank/bruiser.

First of all, let's take a quick look at Varian's three basic abilities, his trait, and his three heroic options.

(Q) Lion's Fang

Mana: 50
Cooldown: 8 seconds
Create a shockwave that travels in a straight line, dealing 150 (+4% per level) damage and Slowing enemies by 35% for 1.5 seconds. Each enemy hit heals Varian for 35, increased to 140 against Heroes.

This ability is fairly straightforward. It should be noted that the skillshot line is thin, so it's not that hard to dodge.
The healing from this ability is actually modest, and when several heroes clump together with some minions you can get massive amounts of health from it. This isn't all, it's also a fairly good source of damage, but it's real power (in my opinion) is the slow. It reduces enemy movement speed by 35% for over a second, allowing for not only retreating from enemies who pursue you, but gaining on enemies who are fleeing from you.
All in all, this ability can be incredibly powerful, and is one of the best in Varian's set. Make sure you practice hitting people with it though, as it can be kind of tricky, especially if your enemy knows what he is doing.

(W) Parry

Mana: 30
Cooldown: 10 seconds
Parry all incoming Basic Attacks for 1.25 seconds, reducing their damage by 100%.
Stores up to 2 charges.

Yet another solid ability. This nullifies Tracer and Illidan for 1.25 seconds, and if you hit the second charge immediately, it can essentially last 2.50 seconds instead!
This is also a good ability if you try to take camps early, as negating that damage can really turn the tides in your favour. If you use it while Zul'jin is attacking with his trait active, he'll deal himself damage and not even get the bonus 25% on you. Basically any hero at all that uses auto attacks as a powerful source of damage can be countered with this ability, but one hero you do have to be careful about, even with this, is Valla, as she attacks not only quickly, but for a lot of damage (especially if she takes Manticore). That being said, she's still not much of a threat.

(E) Charge

Mana: 45
Cooldown: 12 seconds
Charge to the target enemy, dealing 50 (+4% per level) damage and slowing them by 75% for 1 second.

And we cap off Varian's basic abilities with a third one, which is incredibly powerful. The damage is negligible (at least for now), but 75% slow for a whole second is mind blowing. Lunara can't escape now!
This ability is best used right after the slow from Lion's Fang wears off. It's best not used as an opening move, because the damage is low enough it doesn't really matter. This is especially true if you take the Colossus Smash build, as that is a much better opener.

(D) Heroic Strike

Cooldown: 18 seconds
Every 18 seconds, Varian's next Basic Attack deals 125 (+4% per level) bonus Spell damage. Basic Attacks reduce this cooldown by 2 seconds.

This, Varian's trait, is powerful for several reasons. First of all, normal armour doesn't block that bonus damage, and second of all, a whopping 125 extra damage is incredible, the cooldown reduction is just a final cherry on top, making this ability one that allows you to destroy even high-health enemy heroes, like Anub'arak and Cho.

(R1) Taunt

Mana: 20
Cooldown: 16 seconds
Silence a target Hero and force them to attack Varian for 1.25 seconds.
Passive: Maximum Health and Health Regeneration increased by 40%.

In and of itself, this ability is a pretty nifty option. You can drag heroes such as Valla and Illidan off your healer or damage, but the best choice for this is to hit a spellcasting class. Using this on Nova is good, but Valeera is a better target. Perhaps the ultimate option, however, is Kael'thas--he's utterly defenseless, being forced to attack you for 1.25 seconds.
The health and regen bonus is also solid, it allows you to not just pretend to be a tank, but actually be a tank.

(R2) Colossus Smash

Mana: 40
Cooldown: 20 seconds
Smash a target enemy, dealing 160 (+4% per level) damage and lowering their Armor by 20 for 3 seconds, causing them to take 20% increased damage.
Passive: Base Attack Damage increased by 100%.
Passive: Maximum Health reduced by 10%.

The damage on this is okay. It's nothing big, really, but the factor that really makes this talent phenomenal is that armour reduction. This should almost always be your opener if you choose it. It's got a low enough cooldown, and the ability to increase all damage against the target essentially ensures your victory in any one-on-one against a damage or support hero, if you are both the same level.
The damage increase allows you to get upwards of 400 damage at higher levels. The health reduction is unfortunate, but more than a fair price to pay for the benefits. Because of it, however, this should not be your choice unless you have another bruiser who can step into the tank role ( D.Va) or an actual tank ( Diablo).
One thing worth mentioning about this one and Twin Blades of Fury: Colossus Smash is largely a burst talent, Twin Blades of Fury is a steady wear-down talent. Both, of course, are viable damaging choices, but it is key to examine the health-pools of the enemy before making a choice. If they have squishy heroes, go with Colossus Smash, but Twin Blades of Fury if they have massive amounts of health.

(R3) Twin Blades of Fury

Basic Attacks reduce Heroic Strike's cooldown by 9 seconds, and increase Varian's Movement Speed by 30% for 2 seconds.
Passive: Attack Speed increased by 100%.
Passive: Base Attack Damage reduced by 25%.

The first thing that should be said about this is that you can take it even if you have no tank. You can use this talent and still function as your team's damage-soaker, it's not even that hard. We'll cover this more below, in the talents section.
I think the big thing about this talent is not the attack speed bonus--it's the heroic strike change, and the movement speed increase. Nothing can get away from you now, you can slow enemies with Lion's Fang and Charge, and they will not be able to gain on you. Even Lunara cannot escape, whether you use those two abilities or not. The attack speed buff, however, makes this talent into a killer. Every third attack will gain Heroic Strike's bonus damage, which offsets the negative damage.
At level one, Varian's basic attack deals 74 damage. Reduced by 25% equals 55.5. But, you're attacking 1.25 additional times per second, which actually is a net increase to damage, not a decrease. Every two seconds, instead of 185 damage (2.5 • 74 = 185), you're dealing 277.5 damage (5 • 55.5 = 277.5). A huge increase! Now think about the Heroic Strike attack, which is triggering on every 3rd attack, giving you +125 bonus damage, which is happening almost every second (2.5 attacks per second).
Every 6 seconds you will make 15 attacks (2.5/second, 2.5 • 6). That's 832.5 basic attack damage, plus five triggers of Heroic Strike, 625 extra damage, for a total of 1,457.5 damage every 15 seconds. Now throw in that Stim Drone...

Now we'll discuss talents. All the talents will be rated on this 1-to-5 scale:

1/5 -- This talent is horrid; don't ever take it.
2/5 -- This talent is either very bad or extremely situational.
3/5 -- This talent is either okay or situational.
4/5 -- This talent is a solid choice or good in most situations.
5/5 -- This talent is an amazing option or viable in almost every situation.

Here we look at basic attack damage increase talents (except in the case of Overpower, but that affects your basic attack damage anyway).

Lion's Maw 4/5

Quest: Every time Lion's Fang hits a Hero, increase its damage by 6, up to 120.
Reward: After hitting 25 Heroes, the slow is increased to 50% and its duration is increased to 2 seconds.

First off, this is a pretty good talent. The extra damage is good, but it's really the slow that tops it off, making it, especially late-game, a game-changing talent. You go from decent slows to incredible slows, without a pause in between.

Overpower 3/5

When Parry blocks a Hero's Basic Attack, Heroic Strike's cooldown is refreshed and the next one does 40% more damage.

This talent is okay. It's not bad, per se, but it isn't good enough to warrant picking it over either of the other options.
One possible scenario in which this would be good is a Twin Blades of Fury build, but even then this isn't my first choice. This is simply because, as we discussed above, High King's Quest gives so much net bonus damage. Also, Twin Blades of Fury build already gives you Heroic Strike every third auto-attack. Colossus Smash might synergize well with it. Another thing to remember is that this is still a valid option if you take Shield Wall, but the text of the talent is, "Blocks a Hero's Basic Attack." I tested it, and Shield Wall does not cause it to trigger when blocking any damage (which would be cool, but alas).

High King's Quest 4/5

Quest: Hit 50 Heroes with Basic Attacks.
Quest: Participate in 5 Hero Takedowns.
Quest: Gather 15 Regeneration Globes.
Reward: Completing a Quest grants 10 Base Attack Damage. Completing all 3 Quests grants an additional 30 Base Attack Damage.

This talent is always my go-to pick. It's just a good choice, but it becomes an astounding choice when paired with Colossus Smash. The quest takes a bit to finish, but it's worth finishing for that reward. It might seem counter-intuitive to select this if you're going for Twin Blades of Fury, but we already covered how that heroic gives you a massive net increase to damage (92 points!), adding more damage on to that per second can allow you to steadily shred through enemies.

These were already covered in the abilities section, but one thing is worth noting here: Once you hit level four, you will be so much more powerful than everyone else, be fearless about engagement (but not imprudent!). You can, if you play your cards correctly, easily 1v2 at this level, if the enemies are also level four. That being said, do not attempt to do this unless you really know what you're doing! Better safe than sorry, and it could be a setback for your team.

Now we have a series of healing talents, all of them with very powerful regeneration potential.

Lionheart 5/5

Increase Lion's Fang's healing from Heroes by 75%.

This is, simply put, an amazing option. The healing goes from 140 to 245, turning this talent from a situational healing tool to a nearly unstoppable health regen, should multiple enemies clump together. The maximum healing you'll get from this talent is 1,225, if you manage to hit all five of the enemy heroes, but that's unlikely. More often than not, one or two enemies will be hit, which still amounts to a modest heal.

Second Wind 4/5

Basic Attacks heal Varian for 1% of his maximum Health. While below 50% Health, they also heal him for 50% of the damage dealt.

If you took Colossus Smash or Taunt this talent is a solid 1/5, but Twin Blades of Fury turns it into a health pump. You'll be healing 2.5% of your max HP every second when in the thick of combat, plus an additional 50% of damage dealt if you're at low health. This is really the talent that lets Twin Blades of Fury Varian become a tank, allowing you to soak up intense amounts of damage, along with Lion's Fang's heal and Parry's basic attack blocks.
Another way this pairs well with Twin Blades of Fury is the ability you have now to stand on objectives like the shrines in the Dragon Shrine map or the control points in Braxis Holdout and have so much self-heal that enemies cannot get you off of it. You must not get too greedy with this, however, as that can be easy!

Victory Rush 3/5

Every 30 seconds, Varian's next Basic Attack will heal him for 350 (+4% per level) Health. When a nearby enemy Minion or Monster dies, the cooldown is reduced by 10 seconds.

I used to love this talent, until I realized its one downfall: It's unpredictable. This is not a sustainable talent in team fights on objectives, the one place it would be good is when you're pushing a wave and fighting an enemy hero, because the minion deaths will allow you to re-trigger it. All in all, this talent is just not good enough to be better than either of your other options.

Two very powerful talents which can really alter your play style.

Shield Wall 3/5

Parry now grants Protected, preventing all incoming damage while active. Additionally, Parry's cooldown is reduced by 5 seconds, but it loses 1 charge.

"But wait," I hear you say, after seeing the rating I gave this talent, "doesn't it make you immune to damage?"
Well, yes, it does, but the drawbacks are not good enough to make it worth it, in my eyes. The loss of a charge just isn't offset by the two benefits, despite how good they are. One place this would be good is if you're fighting a Kael'thas or Malthael, or some other hero with fatal burst damage. Against Valla, Tracer, and Illidan though? It's just not worth it. One cool synergy to keep in mind is with Ana's Nano Boost. You get to make yourself Protected roughly every 2.5 seconds, which is solid.

Warbringer 4/5

Reduces Charge's cooldown by 8 seconds and Mana cost from 45 to 22. Additionally, Charge can be cast on allied Heroes.

This talent is very good for several reasons. First off, it puts charge on a 4 second cooldown, and makes it so cheap. It becomes a spammable ability, and, unlike Shield Wall there are no drawbacks. You can even flee the fight by casting it on an ally! It's a go-to pick no matter which build you're using. As I said above, however, under certain circumstances Shield Wall may supercede Warbringer--but those circumstances are rare.

Another Charge talent, along with two situational picks.

Juggernaut 3/5

Charge deals bonus damage to Heroes equal to 4% of their maximum Health.

This talent is good, but not great. It's the best pick of the tier, but it isn't a super great pick. The damage isn't very high, but it's still is bonus damage, and it doesn't change based on the enemies current health, like Silver Bullet, but based on the enemies max health, like Manticore, so it's good against heroes like Cho. On the plus side, this synergizes very well with Warbringer's cooldown reduction.

Mortal Strike 3/5

Heroes hit by Heroic Strike receive 40% reduced healing for 4 seconds.

This one isn't great either, but it could work with Twin Blades of Fury. You can keep enemies with that -40% permanently, which can add a severe detriment to their healer, making him push extra hard and expend his mana to no avail.

Shattering Throw 2/5

Activate to throw a sword at a target Hero that deals 50 (+4% per level) damage, and up to 1400 (+4% per level) bonus damage to their Shields.
Passive: Basic Attacks against Heroes deal up to 200% bonus damage to Shields.

This talent is even more situational than the other two of this level, and isn't really a great pick. The one exception is if you are facing Artanis, whose shields you can blast away with either the activation of this ability or simply ramming him with Twin Blades of Fury. Other shielding heroes include Fenix, Johanna, Zarya, and Kerrigan.

Secondary abilities: Banners that buff nearby ally heroes. They can be killed, so keep that in mind.

Banner of Stormwind 3/5

Activate to place a Banner that grants 25% increased Movement Speed to nearby allied Heroes. Lasts 12 seconds.

There's nothing wrong with bonus speed, and this talent is especially beneficial if you do not have Twin Blades of Fury, as this can provide you with the needed boost on your enemy to catch up. A great tool for chasing, if the target is out of range of your slowing abilities.

Banner of Ironforge 3/5

Activate to place a Banner that grants 20 Armor to nearby allied Heroes, reducing damage taken by 20%. Lasts 12 seconds.

This talent is also a good pick, especially if you went with Taunt, as it increases your survivability, as well as that of your allies.

Banner of Dalaran 4/5

Activate to place a Banner that grants 20% increased Spell Power to nearby allied Heroes. Lasts 12 seconds.

This is what I consider to be the ultimate talent when paired with Kel'Thuzad, Kael'thas, or similar casting heroes. The damage such mage heroes can deal is incredibly high ( Kel'Thuzad coming in with 105% Spell Power after he finishes his quest, over doubling damage dealt). It certainly doesn't hurt you either. A solid option for this tier.

Good ol' Storm Talents, some more powerful than others. If you reach this level first, the enemy will easily fall before you.

Vigilance 2/5

Being hit by a Hero Basic Attack reduces the cooldown of Taunt by 1 seconds.

This talent isn't horrid, but it's not very good, either. Maybe against Tracer or someone else who basic attacks rapidly, but this just isn't a valid pick in most scenarios, compared with your other two options.

Master at Arms 4/5

Colossus Smash affects all enemies near the target, and its cooldown is reduced by 10 seconds.

An incredible talent which allows you to lower the target's armour by 20% for 3 seconds every 10 seconds. The AOE addition just turns it into a phenomenal choice. If you took Colossus Smash, this is definitely the talent to go for.

Frenzy 4/5

Basic Attacks increase Movement Speed by an additional 10%. Increases the damage of Heroic Strike by 25%.

Another solid pick. This allows you to pump out insane damage, and even Tracer can't escape from you now, with your incredible speed increase. This is the talent for you if you took Twin Blades of Fury.

Glory to the Alliance 3/5

Banner now also increases health regeneration and all healing received for nearby allied Heroes by 50%, and the cooldown is reduced by 50%.

This certainly isn't a bad option, but I wouldn't pick it if I didn't take Taunt at level four. Increases not only health regen, but all healing received, making it a lot easier for healers to do their thing. Lúcio can heal a ton with this talent, it definitely increases your team's teamfight survivability chance.

Demoralizing Shout 3/5

Activate to demoralize nearby enemy Heroes, reducing damage they deal by 40% for 5 seconds.

This is your second option if you have Taunt. I've never really seen its appeal over Glory to the Alliance, but if your surrounded by enemies hitting this and then Lion's Fang can make your survival chance skyrocket.

Now let's consider some good allies to have.

Thank you so much for reading this all the way to the bottom (if you did)! I plan to add more things later, including expanding the threat list, and possibly adding maps/heroes Varian works well with. Stay tuned for such details, and please leave your suggestions, criticisms, and errors you found in the guide in the comments section!

December 3rd, 2021

Updated the threats, and fiddled around with some formatting/phraseology. Nothing big yet!

June 9th, 2021

Modified the pros/cons of Twin Blades of Fury slightly. Expect a big(ish) update soon!

April 16th, 2021

Added extra threats.

March 25th, 2021

Added information about talents and threats.

March 14th, 2021

Updated threats.

March 6th, 2021

Added info about Abathur in the Twin Blades of Fury build--I'll get to Taunt eventually!

February 23rd, 2021

Fixed Second Wind's icon and link (was previously Second Wind).

February 17th, 2021

Added more threats.

February 16th, 2021

Added more depth to the Twin Blades section, as well as fleshed out the C-Smash section.

December 29th, 2020

Changed the name of the guide.

December 24th, 2020

Changed the talent format; changed the pros/cons.

December 19th, 2020

Changed the talent format; added information to the general talent tier synopses; added a changelog; added pros/cons.