Robots that have different forms and capabilities are used in a wide variety of situations; however, one common point to all robots interacting with humans is their ability to communicate with them. In addition to verbal communication or purely communicative movements, robots can also use their embodiment to generate expressive movements while achieving a task, to convey additional information to its human partner. This article surveys state-of-the-art techniques that generate whole-body expressive movements in robots and robot avatars. We consider different embodiments such as wheeled, legged, or flying systems and the different metrics used to evaluate the generated movements. Finally, we discuss future areas of improvement and the difficulties to overcome to develop truly expressive motions in artificial agents.