Cellular membranes undergo continuous remodeling. Exocytosis and endocytosis, mitochondrial fusion and fission, entry of enveloped viruses into host cells and release of the newly assembled virions, cell-to-cell fusion and cell division, and budding and fusion of transport carriers all proceed via topologically similar, but oppositely ordered, membrane rearrangements. The biophysical similarities and differences between membrane fusion and fission become more evident if we disregard the accompanying biological processes and consider only remodeling of the lipid bilayer. The forces that determine the bilayer propensity to undergo fusion or fission come from proteins and in most cases from membrane-bound proteins. In this review, we consider the mechanistic principles underlying the fusion and fission reactions and discuss the current hypotheses on how specific proteins act in the two types of membrane remodeling.