Deep learning (DL) has seen tremendous recent successes in many areas of artificial intelligence. It has since sparked great interests in its potential use in power systems. However, success from using DL in power systems has not been straightforward. Even with the continuing proliferation of data collected in the power systems from, e.g., synchrophasors and smart meters, how to effectively use these data, especially with DL techniques, remains a widely open problem. This chapter shows that the great power of DL can be unleashed in solving many fundamentally hard high-dimensional real-time inference problems in power systems. In particular, DL, if used appropriately, can effectively exploit both the intricate knowledge from the nonlinear power system models and the expressive power of DL predictor models. This chapter also shows the great promise of DL in significantly improving the stability, resilience, and security of power systems.