The electric power system is currently undergoing a period of unprecedented changes. Environmental and sustainability concerns lead to replacement of a significant share of conventional fossil fuel-based power plants with renewable energy sources. As a result of this energy transition, centralized bulk generation based on fossil fuel and interfaced with synchronous machines is substituted by distributed generation based on renewables and interfaced with power electronic converters. Accordingly, the entire operation of power systems is undergoing several major paradigm shifts: from decentralized device-level control, over distributed coordination of energy sources, to real-time system-level optimization, and open markets involving demand response and energy storage. In this article, we give a tutorial introduction to new and emerging thrusts in analysis, control, and optimization of future, smart, and cyber-enabled power systems. The solutions that we present tap into some recent methodological advances in control and optimization, with a focus on the analysis of multiagent decision scenarios and on the design of decentralized and networked control strategies. We cover the topics of decentralized control of power converters in low-inertia power systems, real-time control of distribution grids, optimal and distributed frequency control of transmission grids, and coordination of energy supply and demand. Throughout the article we also present worthwhile open directions for future research.