WATCH: Medieval MMA Is A Thing
No, medieval MMA doesn't happen in Florida. (You assumed Florida, right?) It's a big deal in Russia and the states of the former USSR. Dudes put on armor, grab a sword and a shield, and proceed to beat each other up in a combination of MMA (mixed martial arts) and HMB (historical medieval battle).
The Telegraph did an in depth piece on it if you're dying to know more.