An Underground Fight is a form of playing Cardfight!! Vanguard in the Anime.
Underground Fights have only appeared in Episode 36. According to Miwa, players are required to bet cards and the rules are ignored. Players are shown to be allowed to do cheating (drawing a card from the middle of the deck instead of the top, changing cards in the hand with cards hidden, etc). Kai started challenging Underground fighters after the summer training camp as additional training, even defeating the current king Jun. Despite being the king, Jun wasn't shown using any tricks or cheating during his fight with Kai.