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Machine learning has the potential to transform how power systems are planned and operated. This talk reviews some recent developments in machine learning for power systems, focusing on the concept of trustworthy optimization proxies that provide approximations to optimization models in milliseconds. The talk presents primal proxies that provide near-optimal feasible solutions to Optimal Power Flow (OPF) and Security-Constrained OPF, and dual proxies that deliver feasible dual bounds to the same problems. These optimization proxies can be integrated into simulation platform that performs, for the time, real-time risk assessment of power systems. At the technical level, the talk reviews the concept of differentiable programming, self-supervised learning, compact optimization learning, and input-convex neural networks. The practicality of the proposed techniques is demonstrated on power systems with up to 30,000 buses.