Optimization problems are ubiquitous in economics. Many of these problems are sufficiently complex that they cannot be solved analytically. Instead economists need to resort to numerical methods. This article presents the most commonly used methods for both unconstrained and constrained optimization problems in economics; it emphasizes the solid theoretical foundation of these methods, illustrating them with examples. The presentation includes a summary of the most popular software packages for numerical optimization used in economics, and closes with a description of the rapidly developing area of mathematical programs with equilibrium constraints, an area that shows great promise for numerous economic applications.