a b s t r a c t P2P overlay networks have attracted significant research interest due to their utility as virtualized abstractions of complex network infrastructures, optimized to satisfy specific criteria, e.g. minimum delay or shortest diameter. In the context of modern pervasive environments, which are characterized by complexity, heterogeneity, dynamicity, and mobility in terms of the underlying networks, the utilization of P2P overlays accordingly offers a series of advantages by countering the aforementioned adverse characteristics. The widespread deployment of pervasive environments and the plethora of proposed P2P systems, both call for a systematic way to study related research works. In this paper we review related research on P2P (peer-to-peer) overlay networks in pervasive environments. In this respect, we therefore analyze relevant requirements and discuss the application and deployment of P2P overlays and systems on top of the networking infrastructures that are supported by pervasive environments. Aspects such as scalability, resource discovery, algorithmic complexity, security, and support for dynamicity are examined for existing research works, in an effort to identify the most suitable P2P overlay for the requirements set by the nature of pervasive environments. We also taxonomize P2P overlays using the well-established classification scheme in regard to their structure or lack of it. Furthermore, we study the notions of multi-layer and bio-inspired P2P overlays that have great synergies with pervasive environments due to their inherent characteristics, especially in terms of flexibility and robustness. By describing and critically analyzing existing systems and discussing current research and open issues, we aim to instigate further research in this domain, while at the same time this work should serve as a point of reference for state-of-the-art P2P overlays in pervasive environments.