The fusion of biomembranes is an ubiquitous event in living organisms encountered in diverse situations, such as intracellular trafficking, recycling, fertilization, and infections by enveloped viruses. Even though each specific type of biological fusion is regulated by particular fusion proteins, it always involves the merger of two lipid bilayers. Even in the absence of proteins, bare lipid bilayers can be induced to undergo fusion. The question whether different types of fusion are variants of one or several universal fusion mechanisms has received much attention, but is not finally answered. At present, the most promising candidate is the stalk‐pore fusion pathway, which involves several lipid‐based fusion intermediates. We give an overview of common fusion types, current knowledge of corresponding fusion mechanisms, and efforts to model membrane fusion. The latter includes both phenomenological modeling and computer simulations.