League of Legends (LoL) Question: What is the best in facing tank matchups

The point of playing tanks is to try and not get literally destroyed. True damage, % penetration ( Last Whisper upgrades or Void Staff) and max health % damage ( Null Zone, Silver Bolts) all work to getting the tanks dying faster.

Kiting them also helps.

Best items?

Lord Dominik's Regards for ADCs/Marksmen. Make sure you get several items before you build it though.

Blade of the Ruined King for anyone that's attack-speed based.

Black Cleaver for melee champions that deal physical damage (usually with abilities).

Void Staff for mages.

Often your champion choice can limit how effective you are at killing tanks though. Look for champions that have % health damage in their kits like Fiora and Vayne.

In all honesty, if you want to destroy top lane tanks, Fiora is a great pick into most tanks. While her very very early game is pretty weak, Fiora is god-tier from levels 6 to 18. Black cleaver and titanic hydra should be sufficient enough for killing just about anybody.

As Falseo said, the idea behind a tank is to not get destroyed. Now if you're matched against them and you want to push an advantage you can go with harder sustain, penetration or %max hp damage.

- Penetration: Abyssal Mask/ Liandry's Torment/ Sorcerer's Shoes if you deal magic damage; Black Cleaver or any of Serrated Dirk's upgrades if you deal physical damage. Last Whisper and Void Staff only work late game, when you got more damage and the tanks got more armor/magic resist.
- Sustain: Any defense item against their type of damage or lifesteal/spellvamp for some champions. Spectre's Cowl's upgrades vs magic damage; Dead Man's Plate/ Sunfire Aegis/ Randuin's Omen vs physical damage; any of Vampiric Scepter's or Hextech Revolver's upgrades if you're dealing lots of damage and want to keep your health up.
- %max hp damage: Blade of the Ruined King for physical damage autoattack based champions or Liandry's Torment for magical damage spell based champions.

In the end, the best way to "destroy" a tank is playing a champion that can counter them. Your best bet is either play a harder tank with better sustain ( Dr. Mundo, Garen) or a really good poke champion to wear them down from a distance ( Quinn, Vladimir, Teemo).

Or you could learn how to play/build against every one of them one by one with each one of your champions, but that would take too long to explain unless you ask for particular matchups (make a forum post instead of a question if you want to ask that).