Findings from diverse fields of study, including neuroscience, psychology, zoology, and sociology, demonstrate that human and non-human primates maintain a representation of the space immediately surrounding the body, known as peripersonal space (PPS). However, progress in this field has been hampered by the lack of an agreed upon definition of PPS. Since the beginning of its formal study, scientists have argued that PPS plays a crucial role in both defensive and non-defensive actions. Yet consensus is lacking about the cognitive and neural instantiation of these functions. In particular, researchers have begun to ask whether a single, unified system of spatial-attentional resources supports both the defensive and non-defensive functions of PPS or, rather, whether there are multiple, independent systems. Moreover, there are open questions about the specificity of PPS. For example: Does PPS dissociate from other well-known phenomena such as personal space and the body schema? Finally, emerging research has brought attention to important questions about individual differences in the flexibility of PPS and the distribution of PPS in front compared to behind the body. In this advanced review, we shed light on questions about the nature of PPS, offering answers when the research permits or providing recommendations for achieving answers in future research. In so doing, we lay the groundwork for a comprehensive definition of PPS. This article is categorized under: Cognitive Biology > Evolutionary Roots of Cognition Psychology > Attention Psychology > Perception and Psychophysics Neuroscience > Plasticity.