Common envelope evolution is the most important phase in the lives of many significant classes of binary stars. During a common envelope phase, the stars temporarily share the same outer layers, with the cores of both stars orbiting inside the same common envelope. This common envelope is sometimes ejected and helps to explain the formation of a wide variety of astrophysical phenomena, including cataclysmic variables, X-ray binaries, progenitors for type Ia supernovae, and gravitational-wa...