We provide a comprehensive review of theoretical and experimental studies of several configurations involving liquid-gas interfaces in contact with heated solid substrates which can be either dry or covered with micro- or nanoscale films. Particular attention is paid to the development and experimental validation of mathematical models for the latter case. The gas phase can be pure vapor or moist air, leading to different limiting mechanisms for heat and mass transfer rates. Evaporation at the liquid-gas interface is coupled together with other relevant physical phenomena such as capillarity, London-van der Waals disjoining pressure, Marangoni stresses, diffusion and fluid flow in the gas phase, electrostatic interactions of interfaces, and vapor recoil. All of these are discussed, with the main focus on how they influence the interface shapes and heat transfer rates near contact lines. In particular, conditions are identified for attaining very large local heat fluxes. Selected topics related to-contact line instabilities and viscous flows with solid particles under conditions of significant evaporation are discussed, followed by an overview of some open questions and possible new research directions. (C) 2016 Elsevier Ltd. All rights reserved.