The power flow equations model the relationship between voltage phasors and power injections at nodes (buses) in an electric power system and are fundamental in their analysis and operation. A wealth of literature exists on these equations, many providing different representations of them. This monograph provides the first comprehensive survey of representations in the context of optimization. To achieve this the power flow representations surveyed are categorized as either relaxations or approximations. The techniques described in here form the basis of running an optimally efficient modern day power system. A Survey of Relaxations and Approximations of the Power Flow Equations is a must-read for all students and researchers working on the cutting edge of electric power systems.