The issue of how to make embodied agents explainable has experienced a surge of interest over the last three years, and, there are many terms that refer to this concept, e.g., transparency or legibility. One reason for this high variance in terminology is the unique array of social cues that embodied agents can access in contrast to that accessed by non-embodied agents. Another reason is that different authors use these terms in different ways. Hence, we review the existing literature on explainability and organize it by (1) providing an overview of existing definitions, (2) showing how explainability is implemented and how it exploits different social cues, and (3) showing how the impact of explainability is measured. Additionally, we present a list of open questions and challenges that highlight areas that require further investigation by the community. This provides the interested reader with an overview of the current state-of-the-art.