The basic properties of individual recurrent nova systems are reviewed, and the mechanisms of their outbursts are studied. Some general properties associated with accretion events and thermonuclear runaway models are briefly examined, and detailed models for the recurrent novae T CrB, RS Oph, T Pyx, U Sco, and V1017 Sgr and the possible recurrent novae WZ Sge, V616 Mon, VY Aqr, RZ Leo, V1195 Oph, and V529 Ori are discussed. The results suggest that the outbursts of U Sco and T Pyx are caused by thermonuclear runaways on the surface of massive white dwarfs, while the outbursts of T CrB and RS Oph are very probably accretion events, initiated by a burst of mass transferred from a giant companion onto a main sequence star. V1017 Sgr fails the model criteria for a recurrent nova, being more properly considered a symbiotic star. V1195 Oph, RZ Leo, VY Aqr, and WZ Sge are assigned to the class of dwarf novae. No evidence is found that V529 Ori has recurred. 228 references.