Membrane fusion has an overarching influence on living organisms. The fusion of sperm and egg membranes initiates the life of a sexually reproducing organism. Intracellular membrane fusion facilitates molecular trafficking within every cell of the organism during its entire lifetime, and virus-cell membrane fusion may signal the end of the organism's life. Considering its importance, surprisingly little is known about the molecular-level mechanism of membrane fusion. Due to the complexity of a living cell, observations often leave room for ambiguity in interpretation. Therefore artificial model systems composed of only a few components are being used to further our understanding of controlled fusion processes. In this critical review we first give an overview of the hypothesized mechanism of membrane fusion and the techniques that are used to investigate it, and then present a selection of non-targeted and targeted model systems, finishing with current applications and predictions on future developments (85 references).