Water/solid interfaces are relevant to a broad range of physicochemical phenomena and technological processes such as corrosion, lubrication, heterogeneous catalysis and electrochemistry. Although many fields have contributed to rapid progress in the fundamental knowledge of water at interfaces, detailed molecular-level understanding of water/solid interfaces comes mainly from studies on flat metal substrates. These studies have recently shown that a remarkably rich variety of structures form at the interface between water and even seemingly simple flat surfaces. In this Review we discuss the most exciting work in this area, in particular the emerging physical insight and general concepts about how water binds to metal surfaces. We also provide a perspective on outstanding problems, challenges and open questions.