Peer‐to‐peer (P2P) overlay networks were developed initially for file sharing such as Napster and Gnutella; but later, they have become popular for content sharing, media streaming, telephony applications, etc. Underlay‐unawareness in P2P systems can result in suboptimal peer selection for overlay routing and hence poor performance. In this paper, we present a comprehensive survey of the research work carried out to solve the overlay‐underlay mapping problems up till now. The majority of underlay‐aware proposals for peer selection focus on finding the shortest overlay routes by selecting nearest nodes according to proximity information. Another class of approaches is based on passive or active probing for provision of underlay information to P2P applications. Some other optimizations propose use of P2P middleware to extract, process, and refine underlay information and provide it to P2P overlay applications. Another class of approaches strive to use ISPs or third parties to provide underlay information to P2P overlay applications according to their requirements. We have made a state‐of‐the‐art review and comparison for addressing the overlay‐underlay mismatch in terms of their operation, merits, limitations, and future directions.