In this talk, we present recent progress towards developing learning-based control strategies for the design of safe and robust autonomous systems. Our approach is to recognize that machine learning algorithms produce inherently uncertain estimates or predictions, and that this uncertainty must be explicitly quantified (e.g., using non-asymptotic guarantees of contemporary high-dimensional statistics) and accounted for (e.g., using robust control/optimization) when designing safety critical systems. We focus on the safety constrained optimal control of unknown systems, and show that by integrating modern tools from high-dimensional statistics and robust control, we can provide, to the best of our knowledge, the first end-to-end finite data robustness, safety, and performance guarantees for learning and control. We further show how this approach can be incorporated into an adaptive polynomial-time algorithm with non-asymptotic convergence rate (regret bound) guarantees. As a whole, these results provide a rigorous and contemporary perspective on safe reinforcement learning as applied to continuous control. We conclude with our vision for a general theory of safe learning and control, with the ultimate goal being the design of robust and high performing data-driven autonomous systems.