This review summarizes, organizes, and compares coupled ocean-atmosphere models of El Ni¿o and the Southern Oscillation (ENSO). The models are arranged in a hierarchy of increasing dynamical complexity, and useful categories for this purpose are (1) conceptual and simple models, (2) intermediate models, and (3) coupled general circulation models (GCMs). Conceptual and simple models illustrate three potentially important mechanisms of ocean-atmospheric interaction in the tropics: the slow propagation of oceanic Rossby waves across the Pacific Ocean: the generation of two equilibrium states (a normal state and an ENSO state) with a trigger that switches the system from one state to the other; and the development of coupled instabilities. Intermediate models develop oscillation in two different ways. In one type, coupled instabilities appear in the western and central ocean, intensify and propagate into the eastern ocean, and eventually dissipate there. In the other, the instabilities are confined to the central and eastern oceans, and oceanic Rossby waves that reflect from the western boundary are involved in the onset and decay of ENSO events. Coupled GCMs have so far had limited success in simulating realistic ENSO events, one reason for this being that even moderate errors in model physics can cause solutions to drift away from realistic climatologies. Nevertheless, ENSO-like oscillations also occur in coupled GCMs, apparently arising from several types of processes. None of the more complex models have yet been shown to have the ability to generate two equilibrium states. ¿1991 American Geophysical Union