Irelia is a champion that you may see used often but not always to her full capabilities. i found some good builds but this one works the best for my playing style.i've also worked with using hextech gunblade instead of ifinity edge just for the spell vamp and life steal along with life steal from bloodthirster and hitten style.

i go with armor pen armor and mag resist runes for this build and then 1 of each in quints but if i wanna go lil more tanky like for ranked games ill go with 2 mag resist quints and an armor quint along with armor marks instead of armor pen. the reason i like armor pen is for her ult it does physical damage so armor penetration helps with the output. sometimes ill put in last whisper instead of infinity edge if im goin against a team thats stackin armor.

For Masteries I go full out tanky which is self explanatory for a tank build.

For items I rush Warmogs with sheen then get thornmail and chalice. turn chalice into Mikaels crucible and get bloodthirster along with tri force. this makes me able to sustain with hitten style blood thirster (or blade ruined king) and the active to Mikaels crucible which i can use on myself or on teamate.

I focus mainly on hitten style and blade surge putting one level in my stun. i do this because hitten style gives durability and true dmg. but bladesurge can be used to chase and it refreshes on kill if u kill with bladesurge. you can change this to fit your own style.

Spells i go with barrier because when used with hitten style and mikeals crucible along with having blade of ruined king or blood thirster you dart hella high in defense. i use this at about half health.

Irelia is very durable but lacks the cc that other tanks have with this it is hard to be a tank and help the team but with this build you deal as much dmg as you can take.
you rely just as much on teamates as any other tank. you can carry, but always think of team first.
with irelia always being nerfed changed and tweaked whenever you can find a good build it makes it hard to get good with her. her ult is very under powered but in teamfights it brings back alot of health. DO NOT USE IT ON ONE CHAMPION UNLESS NEEDED YOU WILL REGRET IT IN THE TEAMFIGHT.

Irelia is very durable and can deal as much as she can take. use this to your advantage. in team fights protect the squishy adc and ap carry as much as possible using your e to slow champions who try focusing them and using Mikeals crucible if needed. use you q to get to or from a fight quickly by attacking minions with it refreshing the cooldown. position yourself as to keep everyone away from your carries you lack the cc, but Irelia is one to be feared.

this is my Irelia Build it works well for me and my team and brings fairly often sometimes even leaving me to carry. with this irelia is nearly invincible, but it does not mean you can play like a noob play smart and stay alive good luck.