The South Pacific Convergence Zone (SPCZ) is a diagonal band of intense rainfall and deep atmospheric convection extending from the equator to the subtropical South Pacific. Displacement of the SPCZ causes variability in rainfall, tropical-cyclone activity and sea level that affects South Pacific island populations and surrounding ecosystems. In this Review, we synthesize recent advances in understanding the physical mechanisms responsible for the SPCZ location and orientation, its interactions with the principal drivers of tropical climate variability, regional and global effects of the SPCZ and its response to anthropogenic climate change. Emerging insight is beginning to provide a coherent description of the character and variability of the SPCZ over synoptic, intraseasonal, interannual and longer timescales. For example, the diagonal orientation of the SPCZ and its natural variability are both the result of a subtle chain of interactions between the tropical and extratropical atmosphere, forced and modulated by the underlying sea surface temperature gradients. However, persistent biases in, and deficiencies of, existing models limit confidence in future projections. Improved climate models and new methods for regional modelling might better constrain future SPCZ projections, aiding climate change adaptation and planning among vulnerable South Pacific communities.