The recent spectrum auctions in Europe have shown that serious problems can arise in auctions where multiple complementary objects are being sold (such as blocks of radio spectrum) that will subsequently be used by the winning bidders to compete against each other in downstream markets. Other important instances of such situations include take-off and landing slots at airports and rights for electricity and gas transmission. We first review some of the theory describing multi-object auctions. We next outline the importance of strategic effects arising in auctions that are followed by competition between the bidders, and the tension arising between various goals such as efficiency and revenue maximization. Although more flexible auction formats can have virtues (particularly in taking into account complementarities), they can also be manipulated by bidders to build market power to the detriment of consumers. We next apply these insights to the recent European UMTS licence auctions. Finally we draw the main conclusions and policy implications.