In the tropical stratosphere, deep layers of eastward and westward winds encircle the globe and descend regularly from the upper stratosphere to the tropical tropopause. With a complete cycle typically lasting almost 2.5 years, this quasi-biennial oscillation (QBO) is arguably the most predictable mode of atmospheric variability that is not linked to the changing seasons. The QBO affects climate phenomena outside the tropical stratosphere, including ozone transport, the North Atlantic Oscillation and the Madden–Julian Oscillation, and its high predictability could enable better forecasts of these phenomena if models can accurately represent the coupling processes. Climate and forecasting models are increasingly able to simulate stratospheric oscillations resembling the QBO, but exhibit common systematic errors such as weak amplitude in the lowermost tropical stratosphere. Uncertainties about the waves that force the oscillation, particularly the momentum fluxes from small-scale gravity waves excited by deep convection, make its simulation challenging. Improved representation of the processes governing the QBO is expected to lead to better forecasts of the oscillation and its impacts, increased understanding of unusual events such as the two QBO disruptions observed since 2016, and more reliable future projections of QBO behaviour under climate change.