Close-binary central stars of planetary nebulae offer a unique tool with which to study the critical and yet poorly understood common-envelope phase of binary stellar evolution. Furthermore, as the nebula itself is thought to comprise the ionised remnant of the ejected common envelope, such planetary nebulae can be used to directly probe the mass, morphology and dynamics of the ejecta. In this review, I summarise our current understanding of the importance of binarity in the formation of planetary nebulae as well as what they may be able to tell us about the common-envelope phase -- including the possible relationships with other post-common-envelope phenomena like stellar mergers, novae and type Ia supernovae.