There are currently 3 options in Colosseum, and are all related to PvP.
Go head to head against another player's team in the game. Although this is considered PvP, these fights are not occurring in real-time.
Colosseum also has a ranking system that rewards you every week on Monday's PDT/PST.
This feature was newly added into the game and is currently still in Beta. Unlike Colosseum, this mode is in real-time.
You are given 3 minutes to go head to head against another opponent.
Don't rely too heavily on a single Hero, as Popular Heroes are banned at the end of every Arena week for 2 weeks.
Friendly Duel is also a real-time PvP mode, without the worries of losing your rank. Go head to head against friends for fun in Friendly Duel.