The paper focuses on the economics of procurement contract awarding and discusses problems and solutions in theory and practice. It reviews advances in auction theory and their potential applications to procurement practice, specifically in the context of public procurement law. The paper highlights the growing importance of public procurement and the challenges posed by the discretionary choices of public officials in contractor selection. It also discusses the limitations of traditional auction theory and the need for new theoretical investigations. The paper addresses four specific topics related to multidimensional auctions in public procurement: defining a proper scoring rule when awarding bodies lack necessary information, coping with information disclosure policies, using contractors' reputations in the awarding process, and controlling the risk of collusion and corruption. The paper concludes by examining the problems related to the evaluation of multidimensional bids and the use of reputation in contract awarding.