In recent years, visual sensors have been quickly improving towards mimicking the visual information acquisition process of human brain, by responding to illumination changes as they occur in time rather than at fixed time intervals. In this context, the so-called neuromorphic vision sensors depart from the conventional frame-based image sensors by adopting a paradigm shift in the way visual information is acquired. This new way of visual information acquisition enables faster and asynchronous per-pixel responses/recordings driven by the scene dynamics with a very high dynamic range and low power consumption. However, the huge amount of data outputted by the emerging neuromorphic vision sensors critically demands highly efficient coding solutions in order applications may take full advantage of these new, attractive sensors' capabilities. For this reason, considerable research efforts have been invested in recent years towards developing increasingly efficient neuromorphic vision data coding (NVDC) solutions. In this context, the main objective of this paper is to provide a comprehensive overview of NVDC solutions in the literature, guided by a novel classification taxonomy, which allows better organizing this emerging field. In this way, more solid conclusions can be drawn about the current NVDC status quo, thus allowing to better drive future research and standardization developments in this emerging technical area.