Electric power systems are critical infrastructure that underlie almost all aspects of modern society. With rapidly increasing quantities of renewable generation and the continuing expansion of electricity markets, electric power systems are undergoing significant changes. New algorithms for optimizing the design and operation of electric power systems are needed in order to enable these transformational changes. After providing a brief introduction to electric power systems, this presentation focuses on recent developments relevant to power system optimization. In particular, this presentation discusses the “power flow equations” which model the physical relationships that exist on electric transmission and distribution systems. An approximate representation of the power flow equations is at the heart of electricity market operations. The errors associated with the power flow approximation result in inefficient utilization of the electric transmission system. This presentation describes a newly developed algorithm that characterizes the largest possible error in the power flows predicted by the approximation. Finally, using another new algorithm, this presentation illustrates the challenges associated with solving power system optimization problems that use the non-approximated power flow equations.