The stratospheric quasi-biennial oscillation (QBO) and the tropospheric Madden–Julian oscillation (MJO) are strongly linked in boreal winter. In this Review, we synthesize observational and modelling evidence for this QBO–MJO connection and discuss its effects on MJO teleconnections and subseasonal-to-seasonal predictions. After 1980, observations indicate that, during winters when lower-stratospheric QBO winds are easterly, the MJO is ~40% stronger and persists roughly 10 days longer compared with when QBO winds are westerly. Global subseasonal forecast models, in turn, show a 1-week improvement (or 25% enhancement) in MJO prediction skill in QBO easterly versus QBO westerly phases. Despite the robustness of the observed QBO–MJO link and its global impacts via atmospheric teleconnections, the mechanisms that drive the connection are uncertain. Theories largely centre on QBO-related temperature stratification effects and subsequent impacts on deep convection, although other hypotheses propose that cloud radiative effects or QBO impacts on wave propagation might be important. Most numerical models, however, are unable to reproduce the observed QBO–MJO relationship, suggesting biases, deficiencies or omission of key physical processes in the models. While future work must strive to better understand all aspects of the QBO–MJO link, focus is needed on establishing a working mechanism and capturing the connection in models.