When Rengar first came out he was a beast (literally). Riot fixed some annoying bugs and gave him some quality of life changes so he became OP. They then proceeded to nerf him into oblivion and haven't really gotten around to balancing him yet. BUT, He is still an amazing assassin if you play him right!
After some discussion with other Rengar players it seems to me that most people try to play Rengar as a Bruiser or an Off-tank. While this is definitely viable, I think he really shines as a hit and fade assassin.

So here it is, my guide to playing Rengar as I think he is meant to be played, a terrifying headhunter that will jump from the bushes and take your teeth as a trophy!

Credits to jhoijhoi for the template, which you can find here.
My brother Brodock for proofreading and giving me some constructive criticism.

Please don't downvote without explaining why. I finally started going back up on my percentage and someone downvoted while I was still revising my guide. The only comments I have are one of my own, my brother being an idiot and one person who actually liked my guide. If you have a problem with my guide feel free to say so. Don't anonymously downvote, that's just rude.

spaaaaaaace

Pros + Unique Passive + Insane Burst + Good Utility + Great Sustain + Has His Own Resource (Ferocity) + Strikes Fear Into The Enemy!

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Cons - Semi-Squishy - No Reliable Gap Closer - Decent Skill Cap - Ultimate Is Countered With Oracles - Slow - Easily Distracted By Shiny Things

We're gonna run 23/7/0 on Rengar. This gives us all the damage boosts and bonus damage to turrets which makes Rengar a split pushing machine. The extra health is always nice and you can decide to throw three points towards armor or MR, your choice as always.

• Greater Quintessence of Attack Damage: AD! Always good always needed.
  
• Greater Mark of Attack Damage: More attack damage!
  
• Greater Glyph of Scaling Magic Resist: Magic Resist for those Squishies that get a spell off before you can stab them dead.
  
• Greater Seal of Armor: Armor for dueling and trading with Melee Bruisers.

Ignite: Always a solid choice on an assassin. Stops healing and gives you a nice way to finish your target.

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Exhaust: This is also good for Rengar since you can jump on them and make sure they won't go anywhere without wasting your Ferocity bonus on Empowered Bola Strike.

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Ghost: Increases your Movement speed by 27% or 35% if you have Summoner's Wrath . The best part is that you can use this during Thrill of the Hunt and not break your stealth.

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Flash: While I used to love Ghost now that I grab Boots of Swiftness instead of CDR boots I prefer to take Flash. You can use this to flash out of a fight then use Thrill of the Hunt and jump back in with full ferocity. Creates massive amounts of confusion!

Rengar doesn't use mana, instead he has his own unique resource called Ferocity. Whenever Rengar lands an ability on an enemy he gains one Ferocity. Reaching 5 bars of Ferocity empowers Rengar's abilities granting them additional effects. Always try to make sure you have 2 or 3 Ferocity by killing minions or jungling. Don't get caught without any Ferocity because then you'll end up dead.

Pretty basic leveling sequence. Max Savagery first since its our main damage dealer. Bola Strike is next since it's the only way you'll catch anyone. Battle Roar is only useful for the defensive stats and the heal which doesn't increase with skill ups. Thrill of the Hunt gets maxed at 6,11 and 15 just like any ultimate.

• UNSEEN PREDATOR: Whenever Rengar is in a bush he gains the ability to leap to any target within 600 range (750 range with 9 stacks on Bonetooth Necklace).
  
  
• SAVAGERY (Q): Rengar's next attack does more damage and increases his attack speed. This ability is why we don't need much attack speed on Rengar. The bonus's from Savagery and Empowered Savagery WILL stack.
  
  
  Scaling
  Physical Damage: 30 / 60 / 90 / 120 / 150 (+1.0 per attack damage)
  Cooldown: 8 / 7.5 / 7 / 6.5 / 6 seconds
  Attack Speed: 30 / 35 / 40 / 45 / 50 %
  
  
  Ferocity Bonus
  With 5 Ferocity Savagery turns into Empowered Savagery which further increases the damage and attack speed bonuses. This is the only(!) ability that has increased damage from Ferocity. Your other ability bonuses are utility only!
  
  
  Scaling
  Empowered Physical Damage: 30 / 60 / 90 / 120 / 150 (+2.0 per attack damage)
  Empowered Attack Speed Bonus: 60 / 70 / 80 / 90 / 100 %
• BATTLE ROAR (W): Rengar roars which deals magic damage and increases his armor and magic resist for a few seconds. This gives us almost all the defense we need in a regular game.
  Scaling
  Cooldown: 15 / 14 / 13 / 12 / 11 seconds
  Magic Damage: 50 / 80 / 110 / 140 / 170 (+0.8 per ability power)
  Bonus Armor & Magic Resistance: 15 / 22 / 29 / 36 / 43
  
  
  Ferocity Bonus
  With 5 Ferocity Battle Roar turns into Empowered Battle Roar and will also heal Rengar for 40 + (20 per level). This is your sustain ability! Do Not be afraid to use this whenever your missing health. If your not running into a team fight you don't need to save your Ferocity.
  
  
  Scaling
  Empowered Battle Roar will heal Rengar for an extra 20 health per level. So at level 1 it heals 60, level 2 80, level 3 100, etc.
• BOLA STRIKE (E): Rengar throws a bola at a single target, slowing them. This is your only ranged ability so if you can't close with them throw this, if they get away Throw This, if you can't reach them for a combo THROW THIS!
  Scaling
  Cooldown: 12 / 11 / 10 / 9 / 8 seconds
  Physical Damage: 60 / 105 / 150 / 195 / 240 (+0.7 per bonus attack damage)
  Slow: 50 / 55 / 60 / 65 / 70 %
  
  
  Ferocity Bonus
  With 5 Ferocity Bola Strike turns into Empowered Bola Strike which will also root the target for 1 second then apply the 2.5 second slow.
  
  
• THRILL OF THE HUNT (R): This is what makes Rengar feel like a true Predator! When activating Thrill of the Hunt Rengar fades into stealth over one second, gains movement speed and starts stacking Ferocity very quickly. While your invisible you can leap to any target as if you were in a bush. Once this ability is maxed and your build is halfway complete Thrill of the Hunt will have a 42(!) second cool down. This makes Rengar terrifying late game since he can use this ability for recon, ganks, regaining Ferocity, escaping and insane map control. This is another thing that you shouldn't be afraid to use often. Yes, it's your ultimate but at a 42 second cooldown you can use it whenever you want!
  
  
  Scaling
  Cooldown: 140 / 105 / 70 seconds
  Vision Radius: 2000 / 3000 / 4000
  Movement Speed Bonus: 20 / 25 / 30 %
  
  Sadly you can't use Thrill of the Hunt in the middle of a fight anymore since whenever you get hit the stealth gets pushed back another second. Jump into a fight, use your combo, run out, Thrill of the Hunt, jump back in. Don't stick around to fight because you won't last long if you do.

• Boots of Swiftness: I used to swear by Ionian Boots of Lucidity but after a few games I noticed that the Boots of Swiftness actually work better and you can get your max CDR by building Zeke's Herald and Spirit Visage.
  
• ZEKE'S HERALDZeke's Herald: A little health, more CDR and life steal, Zeke's Herald is half the stats that Rengar needs.
  
• BONETOOTH NECKLACEBonetooth Necklace: Rengar's unique item. This will give us enough attack damage until we can grab Sanguine Blade. Grab it early to build those stacks!
  
• Sanguine Blade: Highest damage item in the game and more life steal. What's not to love?
  
• Infinity Edge: More Attack Damage, Crit rating and that lovely, lovely passive. Now your Crits do 250% damage instead of 200%.
  

DON'T FORGET TO ENCHANT YOUR BOOTS AT SOME POINT! Furor makes Rengar scary as hell. One second your 20 feet away and he's falling behind the next, he landed his Bola Strike and is on top of you shredding your face off!

As you can see SOTD will bring Rengar back to his pre-nerf awesomeness. You are guaranteed to kill one person. If you build to counter you can easily kill even tanks. I win games with this build constantly! Try to pick this up after you have Sanguine Blade and Boots of Swiftness. Activate it the instant before you jump. It should go SOTD, Q then Empowered Q. Try to make sure you get both Q's off when SOTD is active.

• Frozen Mallet: If your having trouble sticking to your targets and you can't survive long enough to kill one and get out grab the Frozen Mallet. It makes your attacks slow your targets and gives you a lot of health. There's also some AD on there but not enough to make it worthwhile for our Assassin Build. This is more for the health than the AD.
  
• Randuin's Omen: Great against the bruisers that are the bane of Rengar's existence. Armor, Health, and a great passive that give you the edge in a fight. With the active and exhaust you should be able to take apart any AA Bruiser before they realize your winning.
  
• Spirit Visage: Health, Magic Resist and CDR. I usually end up getting this item unless I'm wiping the floor with the enemy team. The health is always nice but if you need a lot grab Frozen Mallet instead. The real reason we get this is the CDR, MR and the passive. Your sustain will go through the roof with this!

• Maw of Malmortius: This is great when you need a tiny bit of defense against AP but don't want to sacrifice damage. This will give you AD, MR and whenever you health goes below 30% you get a shield that will absorb magic damage!
  
• Ravenous Hydra: Lots of AD, second only to Sanguine Blade, more lifesteal will keep your health high without wasting Empowered Battle Roar. The cool part is that now your attacks are AOE (Area of Effect) and you get an active cleave!
  
• Trinity Force: This is an iffy item. I generally won't touch it but some people love it. It works well with your Savagery but honestly you can't use most of the stats. I think it's just better to get more AD.

This is Rengar's personal item that only he can purchase. It is completely optional to purchase and can be sold at any time. You should always get this though. If your careful you can easily build your stacks without even attempting ganks. Once this thing gets fulled stacked Rengar gets really scary. Assists count so if you jump into a teamfight make sure you tag everyone you can.

Bonetooth Stats
5 Attack Damage plus 2 per level. So at level 6 this item gives 17 Attack Damage for 800 gold.
3 Trophies: +10 armor penetration, +5% cooldown reduction
6 Trophies: +25 movement speed
9 Trophies: Rengar's leap gains 150 bonus range.
14 Trophies: Thrill of the Hunt's duration is increased by 3 seconds. Additionally, Rengar's next ability used after activating Thrill of the Hunt generates 1 bonus Ferocity.

Team coordination is possibly the hardest thing to achieve in LoL. If you want to do well as Rengar though you have to learn how to coordinate with your team for ganks. You should never really go into a fight without someone at least nearby. With the smart ping system its immensely easy to let your teammates know what you intend to do quickly.

Coordinate with your team and jump in after the tank has engaged. Try to jump from an awkward or unexpected angle. When your team comes in from the front you should be to the side or behind them. Pick a low health squishy and kill them quickly. After you target is dead or your combo is on cooldown run away. If you didn't kill them run away anyway because you'll come back in a few seconds and continue the fight. Don't stand in the middle of a teamfight because the few spells tossed your way will kill you. Rengar's counter is CC of any kind.

So to repeat: Jump in after the tank, kill your target/blow your cooldowns, then run. Rinse and repeat until you win or lose. Make sure you hit a lot of people with Battle Roar since the assists will help you get stacks on Bonetooth Necklace. Rengar can control a team fight amazingly so long as you keep disappearing and murdering people.

Also remember if the team fight is going badly don't be afraid to run away. There's no point in dying with your team. If you can escape, do it! You want to keep those stacks high on your Bonetooth Necklace. One the same note if you can secure a kill before you die and help your team get away, do it! That's one less person chasing your wounded teammates and you don't lose any stacks.

Farming is the most important thing to Rengar. Don't focus on ganking, just farm and get your CS up. If you stand around in bushes all day waiting for the perfect gank you'll fall behind very quickly and catching up is extremely hard to do. You have an extreme burst early so if you can land it and get the kill do it.

Once you hit six you have a free pass to kill any squishy. Wait for them to be low health or overextended and jump them! Make sure their alone though because a Rengar that has been focused is a dead Rengar.

As you can see I easily win all the games I play. Just follow my guide and you'll dominate the enemy team! Feel free to send me any results of yours and I'll put em up in this section.

The one custom game was a game with my girlfriend. Just pretend its a normal game :D.