Modern power systems are large, distributed, dynamic, uncertain, and complex machines with a wide range of heterogeneous and spatially-distributed electrical components, e.g., distributed energy resources (DERs), electric vehicles (EVs), intelligent switches, and smart meters. With the fast-growing penetration of distributed devices and technologies in electric power systems, advanced communication, computation, and control infrastructures are progressively utilized by stakeholders for substantiating a more efficient, reliable, resilient, sustainable, economic, and secure management of electricity grid. However, a rigorous modeling of complex power system operations is becoming more challenging as distributed, data-oriented, closely-coupled, and highly uncertain components are blended into power systems. With steady advances in communication and computational technologies, e.g., 5G networks and edge-computing, machine learning techniques will evolve as a viable tool to embrace new opportunities and challenges for power system optimization. Machine learning, which is an extension of the artificial intelligence practice in power systems, is portrayed as a data analytic technique that can train computers to complete complicated operation tasks and arrive at credible decisions automatically via a specific learning process. This presentation offers a systematic application of state-of-the-art machine learning techniques in the optimal operation and control of distributed power systems.