This chapter describes a market-based approach to conduct resource allocation problems in computational Grids. Currently, there is a lot of research done on the technical layer of resource allocation. However, the economic allocation of resources is still an open issue in research and, more importantly, in practical application. The focus in this chapter is on existing market mechanisms, which are transferred from different domains. Possible applications in Grid scenarios are discussed. Most promising — but also most demanding - are combinatorial auctions and exchanges that include high bidding complexity. It is demonstrated how such mechanisms can be applied to Grid markets and what obstacles have to be overcome in order to successfully deploy these mechanisms in future resource sharing markets.