The feature that distinguishes markets for exhaustible resources from markets for other resources is that a nonrenewable stock is being discovered, produced, traded, and consumed. Hence, the characterization of this stock or resource base and the factors determining the rate and extent of exploration and exploitation are fundamental to modeling exhaustible resource markets. The chapter discusses the issues that arise in the estimation of cost functions for exhaustible resources and presents alternative strategies that are employed in providing such a characterization. It focuses on practical methods for modeling the supply of exhaustible resources. The chapter discusses equilibrium models; they provide a vehicle for unified analysis of exhaustible resource markets. Improved estimates of the cost functions for exhaustible resources provide an enhanced base for computational equilibrium models. Among the remaining challenges for research on computational equilibrium models are developing improved methods for capturing short-run dynamics and finding improved ways of testing the models. Further integration of the depletable and nondepletable sectors of the models is another area of potential additional research.