The Recharge Oscillator (RO) is a simple mathematical model of the El Niño Southern Oscillation (ENSO). In its original form, it is based on two ordinary differential equations that describe the evolution of equatorial Pacific sea surface temperature and oceanic heat content. These equations make use of physical principles that operate in nature: (i) the air-sea interaction loop known as the Bjerknes feedback, (ii) a delayed oceanic feedback arising from the slow oceanic response to near-equatorial winds, (iii) state-dependent stochastic forcing from intraseasonal wind variations known as westerly wind bursts (WWBs), and (iv) nonlinearities such as those related to deep atmospheric convection and oceanic advection. These elements can be combined in different levels of RO complexity. The RO reproduces ENSO key properties in observations and climate models: its amplitude, dominant timescale, seasonality, and warm/cold phases amplitude asymmetry. We discuss the RO in the context of timely research questions. First, the RO can be extended to account for ENSO pattern diversity (with events that either peak in the central or eastern Pacific). Second, the core RO hypothesis that ENSO is governed by tropical Pacific dynamics is discussed from the perspective of influences from other basins. Finally, we discuss the RO relevance for studying ENSO response to climate change, and underline that accounting for ENSO diversity, nonlinearities, and better links of RO parameters to the long term mean state are important research avenues. We end by proposing important RO-based research problems.

El Niño-Southern Oscillation (ENSO) is the most prominent interannual climate variability in the tropics and exhibits diverse features in spatiotemporal patterns. This paper develops a simple multiscale intermediate coupled stochastic model to capture the ENSO diversity and complexity. The model starts with a deterministic and linear coupled interannual atmosphere, ocean, and sea surface temperature (SST) system. It can generate two dominant linear solutions representing the eastern Pacific (EP) and the central Pacific (CP) El Niños, respectively. In addition to adopting a stochastic model for characterizing the intraseasonal wind bursts, another simple stochastic process is developed to describe the decadal variation of the background Walker circulation. The latter links the two dominant modes in a simple nonlinear fashion and advances the modulation of the strength and occurrence frequency of the EP and the CP events. Finally, cubic nonlinear damping is adopted to parameterize the relationship between subsurface temperatures and thermocline depth. The model succeeds in reproducing the spatiotemporal dynamical evolution of different types of ENSO events. It also accurately recovers the strongly non-Gaussian probability density function, the seasonal phase locking, the power spectrum, and the temporal autocorrelation function of the SST anomalies in all the three Niño regions (3, 3.4 and 4) across the equatorial Pacific. Furthermore, both the composites of the SST anomalies for various ENSO events and the strength-location bivariate distribution of equatorial Pacific SST maxima for the El Niño events from the model simulation highly resemble those from the observations.