The unit commitment problem is a fundamental problem in the operation of power systems. The purpose of unit commitment is to minimize the system-wide cost of power generation by finding an optimal power production schedule for each generator while ensuring that demand is met and that the system operates safely and reliably. This problem can be formulated as a mixed-integer nonlinear optimization problem, and finding global optimal solutions is important not only because of the significant operational costs but also because in competitive market environments, different near-optimal solutions can produce considerably different financial settlements. At the same time, the time available to solve the problem is a hard constraint in practice. Hence unit commitment is an important and challenging optimization problem. This chapter provides an introduction to the basic problem from the point of view of optimization, summarizes several related modeling developments in the recent literature while providing some possible directions for future research, and concludes with a mention of extensions to the basic problem that have great practical importance and are driving much current research.