Safety-critical control is one of the fundamental problems in autonomous systems. A special class of autonomous systems is the class of hybrid dynamical systems, which involves both continuous dynamic flow and discrete dynamical mode jumps for state evolution. I will introduce how to synthesize safe controllers for hybrid dynamical systems based on local control barrier functions (CBFs), and such a framework enjoys flexibility, non-conservativeness, and computational advantage compared with existing safety-critical methods. Then, I will show how to learn local CBFs for hybrid systems through self-supervision techniques. Finally, I will briefly share some ideas on learning safe and adaptive controllers in multi-agents systems.