Socially interactive robots provide entertainment, information, and/or assistance; this last category is typically encompassed by socially assistive robotics. In all cases, such robots can achieve their primary functions without performing functional physical work. This monograph reviews the existing work that explores the role of physical embodiment in socially interactive robots. This class consists of robots that are not only capable of engaging in social interaction with humans, but are using primarily their social capabilities to perform their desired functions. This monograph explores the embodiment hypothesis that physical embodiment has a measurable effect on performance and perception of social interactions in socially interactive robotics. It presents a thorough review of existing work and analyzes existing results and approaches to embodiment to determine the current state of the embodiment hypothesis. This monograph is a comprehensive and in depth overview of embodiment in socially interactive robots that is a starting point for researchers and students beginning their own research in the area.