The entrainment assumption, originally developed to describe mixing of miscible fluid pairs, has been used successfully in previous investigations to predict the liquid inflow velocity at the boundary of gas or vapour jets submerged in liquids. In this paper, the power of the entrainment assumption is further revealed by the application of the Ricou-Spalding form of the assumption to the breakup of drops and jets in liquid and gas surroundings, and to liquid entrainment from initially stratified two-phase regions.