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Genres are currently supported in MusicBrainz as part of the tag system.
Some tags (the ones in the genre list) are automatically read and presented as genres. The list is expanded according to user requests, so if you feel a genre is missing, request it by adding a style ticket with the "Genres" component.
Genres are subjective, so just like with any other tags, you can upvote and downvote genres you agree or disagree with on any given entity, and you can also submit genre(s) for the entity that no one has added yet.