The Southern Ocean greatly contributes to the regulation of the global climate by controlling important heat and carbon exchanges between the atmosphere and the ocean. Rates of climate change on decadal timescales are therefore impacted by oceanic processes taking place in the Southern Ocean, yet too little is known about these processes. Limitations come both from the lack of observations in this extreme environment and its inherent sensitivity to intermittent processes at scales that are not well captured in current Earth system models. The Southern Ocean Carbon and Heat Impact on Climate programme was launched to address this knowledge gap, with the overall objective to understand and quantify variability of heat and carbon budgets in the Southern Ocean through an investigation of the key physical processes controlling exchanges between the atmosphere, ocean and sea ice using a combination of observational and modelling approaches. Here, we provide a brief overview of the programme, as well as a summary of some of the scientific progress achieved during its first half. Advances range from new evidence of the importance of specific processes in Southern Ocean ventilation rate (e.g. storm-induced turbulence, sea–ice meltwater fronts, wind-induced gyre circulation, dense shelf water formation and abyssal mixing) to refined descriptions of the physical changes currently ongoing in the Southern Ocean and of their link with global climate. This article is part of a discussion meeting issue ‘Heat and carbon uptake in the Southern Ocean: the state of the art and future priorities’.