An energy-efficient water evaporation process uses a falling film evaporator having a plurality of substantially vertical and equidistant heat exchange elements made of a synthetic polymeric material. Each evaporating surface is in contact with a liquid spreading means, and each heat exchange element is heated by steam having a condensation temperature slightly higher than the boiling point of the aqueous solution from which water is being evaporated. Steam formed by evaporation of water either is recompressed and reintroduced as heating steam in a single-stage process or is used as heating steam for another stage, operating at a lower temperature and pressure, in a multistage process. Heating steam condenses to fresh water, which is recovered. This process is operated at a low feed rate, preferably below 45 Kg of incoming aqueous solution per linear meter of horizontal width of each evaporating surface, and is capable of providing a 50% fresh water recovery per pass from sea water. Higher recoveries are possible in the case of brackish waters and various industrial waters. The process is useful in water desalination and purification.