Cellular membranes can form two principally different involutions, which either exclude or contain cytosol. The 'classical' budding reactions, such as those occurring during endocytosis or formation of exocytic vesicles, involve proteins that assemble on the cytosol-excluding face of the bud neck. Inverse membrane involution occurs in a wide range of cellular processes, supporting cytokinesis, endosome maturation, autophagy, membrane repair and many other processes. Such inverse membrane remodelling is mediated by a heteromultimeric protein machinery known as endosomal sorting complex required for transport (ESCRT). ESCRT proteins assemble on the cytosolic (or nucleoplasmic) face of the neck of the forming involution and cooperate with the ATPase VPS4 to drive membrane scission or sealing. Here, we review similarities and differences of various ESCRT-dependent processes, with special emphasis on mechanisms of ESCRT recruitment.