Ocean convection is a key mechanism that regulates heat uptake, water-mass transformation, CO2 exchange, and nutrient transport with crucial implications for ocean dynamics and climate change. Both cooling to the atmosphere and salinification, from evaporation or sea-ice formation, cause surface waters to become dense and down-well as turbulent convective plumes. The upper mixed layer in the ocean is significantly deepened and sustained by convection. In the tropics and subtropics, night-time cooling is a main driver of mixed layer convection, while in the mid- and high-latitude regions, winter cooling is key to mixed layer convection. Additionally, at higher latitudes, and particularly in the sub-polar North Atlantic Ocean, the extensive surface heat loss during winter drives open-ocean convection that can reach thousands of meters in depth. On the Antarctic continental shelf, polynya convection regulates the formation of dense bottom slope currents. These strong convection events help to drive the immense water-mass transport of the globally-spanning meridional overturning circulation (MOC). However, convection is often highly localised in time and space, making it extremely difficult to accurately measure in field observations. Ocean models such as global circulation models (GCMs) are unable to resolve convection and turbulence and, instead, rely on simple convective parameterizations that result in a poor representation of convective processes and their impact on ocean circulation, air–sea exchange, and ocean biology. In the past few decades there has been markedly more observations, advancements in high-resolution numerical simulations, continued innovation in laboratory experiments and improvement of theory for ocean convection. The impacts of anthropogenic climate change on ocean convection are beginning to be observed, but key questions remain regarding future climate scenarios. Here, we review the current knowledge and future direction of ocean convection arising from sea–surface interactions, with a focus on mixed layer, open-ocean, and polynya convection.