Abstract: This talk describes ongoing research at Caltech on integrating learning into the design of safety-critical controllers for dynamical systems. To achieve control-theoretic safety guarantees while using powerful function classes such as deep neural networks, we must carefully integrate conventional control principles with learning into unified frameworks. I will present two paradigms: integration in dynamics modeling and integration at the policy/controller design. A special emphasis will be placed on methods that both admit relevant safety guarantees and are practical to deploy.