Conversational agents have gained widespread popularity due to their ability to simulate and sustain contextual conversations. Prior works predominantly focused on computational challenges. However, avatars — the representation of the agent — impact user interactions and perception of conversational agents’ trustworthiness and usefulness. Despite their importance, we lack a holistic understanding of conversational agent avatar design space. In this work, we address this gap by defining a categorization of 10 dimensions that is based on the analysis and iterative coding of 266 conversational agent papers from 160 venues spanning 2003 to the present. In addition, we built an interactive browser to facilitate exploration and interaction with these dimensions and their interrelationships. Our categorization lays the groundwork for researchers, designers, and practitioners to discern task-specific and contextual aspects of conversational agent avatar design. Our work fosters innovative ideas to facilitate new interactions with avatars by surfacing current patterns and highlighting open challenges.