Even though auctions are capturing an increasing share of commerce, they are typically treated in the theoretical economics literature as isolated. That is, an auction is typically treated as a single seller facing multiple buyers or as a single buyer facing multiple sellers. In this paper, we review the state of the art of competition between auctions. We consider three different types of competition: competition between auctions, competition between formats, and competition between auctioneers vying for auction traffic. We highlight the newest experimental, statistical and analytical methods in the analysis of competition between auctions.