AoE comps ftw

Nasus and Karthus

Or avoid engaging them in teamfights, and send someone to bd if you expect a fight to break out

the reason the meta has always leaned in this direction is because it has so few counters...

IMO some of the only ways it can be done are focused on extreme cc, anti-tank dps, and good pushing.
Kog, Warwick, Nasus, and Poppy are good examples of anti-tanks due to the nature of their abilities.
These characters along with team-stacking items like Madred's and Deathfire Grasp can work out pretty well, but ultimately the best way to counter a tanky team is to try to end the game early (so as to not let them get too tanky, obv).

Kog'Maw or trist with Bloodrazor. I've had a few games playing trist where her range+attack speed has allowed me to tear up a 6 stack cho with warmogs in seconds. It's a lot of fun. and kog with it does, like, 10% of your health for a short period of time.

Deathfire grasp on mages/support
Razors on carries.

Just tried it out recently and it's just amazing how you can just ignore the turrets, it's like you can just steamroll the other team and it's way too OP (I usually don't use that word, but it clearly is in its current state).

I think there should be some kind of scaling of turret's power based on HP / Armor / MR of opponents, don't know what you could do otherwise to make these teams less steamrolling.

Worst case is if you pack Fortify, you can just totally obliterate their pushing power without sacrificing all that much in summoner spells.

Riot should do something about it.

Slows, Cleanse, Bloodrazor/Last Whisper on carries, resists, Fortify to help get you through early game.

Farm, farm, farm, farm. You have to out-farm them. You scale, they don't. Play to that strength.

Mumu and **** lots of Armor/Magic pen

you can beat them if you push early game after mid, you ****ed no matter what you use.

teemo + AS+ bloodrazor rips tanks apart