Guaranteeing safe and reliable control for autonomous robots remains a central challenge, especially in unstructured and uncertain environments. To succeed, robots require methods that combine formal notions of safety and stability with the adaptability of learning-based approaches. In this talk, I will present new control methods that integrate tools from control theory, robust and distributionally robust optimization, and deep learning. I will introduce extensions of control barrier and Lyapunov functions that enable robots to operate safely under imperfect perception and dynamics. I will then describe distributionally robust control formulations that address uncertainty in obstacle motion, localization, and sensor noise within a unified framework. Finally, I will present a generalized Lyapunov approach for certifying the stability of neural controllers, including reinforcement learning policies. I will conclude with a vision for next-generation robotic systems that operate with dexterity and agility while providing certifiable and interpretable notions of safety, stability, and robustness.