Previous chapters consider different auction formats, understood as mechanisms to allocate an object among different individuals (bidders). Each of them is, essentially, characterized by an allocation rule (who gets the object) and a payment rule (how much each bidder has to pay when winning the object and otherwise). In this chapter, we take a more general approach by considering a richer set of mechanisms, seeking to: (1) allocate the object to the individual with the highest valuation (efficiency); (2) maximize the seller’s expected revenue; (3) maximize the social planner’s welfare function; or (4) a combination of these objectives.