Many applications require repeatedly solving a family of optimization problems as parameters vary, which can be computationally prohibitive in real time. This motivates optimization proxies: learned mappings from problem parameters to approximate solutions that can be evaluated rapidly. Optimization proxies are learned by parameterizing the solution map within a function class and training via a single data-driven stochastic optimization problem, an approach that has seen strong empirical success across domains. The seminar discusses the interplay between architecture design, training distributions, training algorithms, and robustness guarantees.