In Sweden there are many different "medieval markets". The largest is the one in Gotland. In Szeklerland, Transylvania are many Hun, szekler knight, early Hungarian and hussar reenactment groups and camps.
It is usual to fight using more restricted target areas than in a real fight and with less speed and force, although some systems try to get as close to real combat as possible. Many societies try to reenact actual battles.