This article provides an overview of evolutionary robotics techniques applied to online distributed evolution for robot collectives, namely, embodied evolution. It provides a definition of embodied evolution as well as a thorough description of the underlying concepts and mechanisms. This article also presents a comprehensive summary of research published in the field since its inception around the year 2000, providing various perspectives to identify the major trends. In particular, we identify a shift from considering embodied evolution as a parallel search method within small robot collectives (fewer than 10 robots) to embodied evolution as an online distributed learning method for designing collective behaviors in swarm-like collectives. This article concludes with a discussion of applications and open questions, providing a milestone for past and an inspiration for future research.