Display omitted •Membrane-based enthalpy exchanger for simultaneous heat and water recovery.•Indirect contact of two gas phase streams in non-isothermal enthalpy exchangers.•Classical and newly developed membranes and modules for water and heat recovery.•Waste heat recovery from flue gas/natural gas in addition to classic air-to-air applications.•Mechanisms of water recovery depending on membrane type and operating conditions. Membrane-based gas-to-gas enthalpy exchangers have a significant position in energy recovery systems, especially in building ventilation. Membrane-based heat exchangers are similar in design to sensible heat exchangers, with a semi-permeable membrane instead of solid interface plates to recover sensible heat and moisture simultaneously. In the present work, all aspects affecting the non-isothermal performance of gas-to-gas membrane heat exchangers have been investigated. These include the effects of membrane core type and properties, moisture transfer mechanisms, module geometry, ways to increase sensible and latent heat recovery efficiency, and the use of these devices in ventilation systems under all climate conditions, other waste heat recovery applications, and industrial systems. Novel membranes, module geometries, and flow configurations developed for this purpose are also presented in this paper. In addition to state of the art in the enthalpy heat exchangers, the outlook and further suggestions are provided.