In a majority of my ranked matches, the enemy jungler is usually a tank jungler. What tends to happen is that they get ahead, and they're too tanky to fight even when the odds are in our favor. My question is, how do I deal with tank junglers especially when they have an ability that scales off of health?
itemize against them.
alternatively you could try to counter jg and get them waayyy behind.
Trundle and Master Yi (bruiser build) hard counter tanks.
is amazing against tanks because he can either dodge or facetank their CC and then melt them with true damage and armor piercing %damage, dealt at 2.5 attacks per second even with just 2 AS items thanks to runes and his steroids.
melts tanks like nothing as well, thanks to his armor/MR/HP stealing ult and massive steroids (also % health damage dealt at 2.5 attacks per second)
I mostly play jungle. What I'm hearing is that until late game, tanks are just gonna faceroll me.
Either find a way to put them behind early so they do not get tanky as quickly or get the person on your team with the best sustained damage ahead so they will be able to kill a tank in a reasonable time span.
Ultimately, you beat tanks by your team being able to kill them in a reasonable time frame without burning any significant cool downs on them.
A rush of on your teams marksman can help if the tank line is getting defense faster than your marksman is finishing damage items as a quick bandage, but having a high enough damage output to deal with tanks without is better. It merely normalizes the time taken based on the difference between your damage and their HP... and can be worse than other options when your damage is sufficiently high relative to their HP.
If you are an AD jungler, 
can help if enemy tanks are building lots of armor.
Forget building against them, the absolute best way to make a tank jungle cry is to counter jungle them HARD. I have been playing tank junglers since about this time last year, and I will say, they are only as weak or strong as your opponent lets them be. One game I was playing Maokai jungle (pre-rework) and at that point he was VERY vulnerable early game, but since their Jarvan didn't counter jungle me once all game, I was able to ramp up into an absolute behemoth, which should not have happened. In another game, I was playing as the new Sion in the jungle. He like all tanks is vulnerable to invade, and this game the enemy Tryndamere jungle knew that and stole ~70% of my camps and left me helpless for most of the game.
The really strong tanks right now (like Sejuani, Sion, and Nautilus) all scale very well, very fast, so you have to invade them from the get go. have someone ward one buff, and you ward their other buff, and as soon as you see them near one buff go to the other one. Have smite ready and wait for them to get low and get the camp low too. Smite steal it and then try to kill them. If you can kill them, great! If not, then you will usually force them to back, during which time you want to kill every one of their camps except for one small monster each, so that they don't respawn. Keep tabs on their buffs and steal them whenever they are up and the tank is either low or in a different part of the map.
If you can't counter jungle like that, then your best bet is to get your lanes fed and farm up hard yourself, and try to shut down their lanes and watch for countergank opportunities. If you are an AP jungle, build a Liandry's, if you are AD, build a BotRK. If you aren't jungling and their tank gets rolling, rush your penetration item ASAP, and/or get your tenacity items.
Counterjungling is and always will be the best way to shut out a tank, but building around it can be useful in a pinch.
EDIT: . This guy right here is also specifically designed to literally eat tanks and steal everything that makes them strong. If their tank gets fed, you as Trundle naturally get fed even more because you take the stats they build for yourself via Q and R. That and he is also an exceptional duelist and counterjungler, which are the two things that shut down tanks the hardest, since they are weak 1v1 and weak to invade.
try out trundle in the jungle, he worked top lane to counter the tanky top lane meta awhile back
he could be the solution now.
Trundle in the Jungle.
So, to update my situation, I've found that Shyvana is really great for countering tank junglers. I can invade them very early, and I know I can outduel them. I've found that Gragas is also not too bad against hard engage tank junglers, like Sejuani or Sion. It just messes up their engage. Any more info aside from banning them is appreciated.
They build a lot of health due to abilities scaling off it? (it's a worthy substitute for BT if there's a troublesome tank)
They have a lot of armor and you're the adc/apc? 
They have a lot of armor/MR and you're just a fighter/tank? 
There's a few options. Just itemize against them. No matter your role, this is an important part of the game.
