Auctions are key mechanisms for allocating scarce resources among multiple parties. While traditionally auctions have mainly been applied to the selling of physical goods, they are becoming increasingly popular as mechanisms for such diverse tasks as procurement, bandwidth allocation, or selling online ad space. At the same time, privacy is a crucial issue in electronic commerce. A major reason why people may be hesitant to use software agents, or to participate in Internet commerce themselves, is the worry that too much of their private information is revealed. Furthermore, in the modern electronic society, the information might get propagated to large numbers of parties, stored in permanent databases, and automatically used in undesirable ways. This chapter studies the possibility of executing the most common types of sealed-bid auctions in a way that preserves the bidders’ privacy.