No there is no governing body, there are different countries who have bodies that grant boxing licenses i.e. to fight in Britain you need a British boxing license and in America you can be granted a license by the governing body in that state, but it`s badly organized, Ali was given a license or go ahead to fight Larry Holmes even though he failed that states medical test, he couldn`t even touch his nose or stand on one leg during the exam because he alrady had Parkinsons disease and former light welter legend Aaron Pryor got a license for a comeback in the 90`s even though he was blind in one eye! Joe Frazier was also more or less blind in one eye his whole career he was never given a vision test at te start of his career though I think medical tests by governing bodies are much more strict now.
