Body-part-centered response fields are pervasive in single neurons, functional magnetic resonance imaging, electroencephalography and behavior, but there is no unifying formal explanation of their origins and role. In the present study, we used reinforcement learning and artificial neural networks to demonstrate that body-part-centered fields do not simply reflect stimulus configuration, but rather action value: they naturally arise from the basic assumption that agents often experience positive or negative reward after contacting environmental objects. This perspective successfully reproduces experimental findings that are foundational in the peripersonal space literature. It also suggests that peripersonal fields provide building blocks that create a modular model of the world near the agent: an egocentric value map. This concept is strongly supported by the emergent modularity that we observed in our artificial networks. The short-term, close-range, egocentric map is analogous to the long-term, long-range, allocentric hippocampal map. This perspective fits empirical data from multiple experiments, provides testable predictions and accommodates existing explanations of peripersonal fields.