Optimization proxies are machine learning models that, given an optimization instance data, seek to predict a close-to-optimal solution for that instance. Such models have received a lot of attention in power systems for their potential to speedup optimization algorithms and enable fast ML-based simulations. Two major challenges in training proxies are costly data-generation, and ensuring that predicted solutions satisfy physical and engineering constraints. This talk presents some recent work in addressing these two challenges for unit commitment and optimal power flow problems. Numerical results are reported on industry-size instances.