Receptor-ligand bonds strengthened by tensile mechanical force are referred to as catch bonds. This review examines experimental data and biophysical theory to analyze why mechanical force prolongs the lifetime of these bonds rather than shortens the lifetime by pulling the ligand out of the binding pocket. Although many mathematical models can explain catch bonds, experiments using structural variants have been more helpful in determining how catch bonds work. The underlying mechanism has been worked out so far only for the bacterial adhesive protein FimH. This protein forms catch bonds because it is allosterically activated when mechanical force pulls an inhibitory domain away from the ligand-binding domain. Other catch bond-forming proteins, including blood cell adhesion proteins called selectins and the motor protein myosin, show evidence of allosteric regulation between two domains, but it remains unclear if this is related to their catch bond behavior.