In recent years the Walrasian general equilibrium model has become an important tool for applied work in such fields as development economics, international trade, macroeconomics, and public finance. This chapter discusses that economic equilibria are usually solutions to fixed point problems rather than solutions to convex optimization problems. This leads to two difficulties that are closely related: first, equilibria may be difficult to compute; second, a model economy may have more than one equilibria. The chapter explores these two issues for a number of stylized economies and analyzes economies with infinite numbers of goods, economies in which time and uncertainty play important roles. Studying economies of this sort is interesting not only for its own sake but also because of the insights it provides into the properties of economies with large but finite numbers of goods. Finally, the chapter extends an analysis to economies that include distortionary taxes and externalities.