Auction theory has evolved in two waves of innovation. The first wave, from the 1960s to the 1980s, focused on single-item auctions and established key principles like revenue equivalence. The second wave, starting in the 1990s, explored multi-item auctions, including different types like pay-as-bid and uniform-price auctions. Researchers have also looked into dynamic auctions and efficient auction design. Progress has been made in understanding how auctions work, but there are still challenges to address.