Dynamic optimization models decisions over time, using either continuous or discrete formulations. This chapter introduces optimal control theory and dynamic programming, with an emphasis on economic applications such as consumption smoothing and investment. Concepts like the Hamiltonian and Pontryagin’s maximum principle (for dynamic optimization in continuous time) and Bellman equations and the Hamilton–Jacobi–Bellman approach (for dynamic optimization in discrete time) are introduced within an accessible and intuitive way. This chapter highlights how intertemporal trade-offs can be rigorously described, modeled and solved, providing a framework for the analysis of long-term policy and planning problems.