The papers in this special section focus on complex systems within current smart grid operations. The existing power grids, being recognized as one of the significant engineering accomplishments, work exceptionally well for the purposes they have been designed to achieve. Enabled by the advances in sensing, communication, computation, and actuation, smart power are rapidly growing in scale, inter-connectivity, and complexity. Major paradigm shifts in power grids include departing producer-controlled structures and transforming to more decentralized and consumer-interactive ones, being more distributed in electricity generation, enhancing the coupling between the physical and cyber layers, and operating in more variable and stochastic conditions. Driven by these emerging needs, power grids are anticipated to be complex and smart networked platforms in which large volume of high-dimensional and complex data is routinely generated, exchanged, and processed for various monitoring, control, and scheduling purposes. The papers in this section cover some of the recent research in the theory of complex systems with applications to power grid operations, which present novel research contributions in all aspects of complex and large-scale systems of relevance and significance in power grids.