The Southern Ocean is a major sink of atmospheric CO2, but the nature and magnitude of its variability remains uncertain and debated. Estimates based on observations suggest substantial variability that is not reproduced by process-based ocean models, with increasingly divergent estimates over the past decade. We examine potential constraints on the nature and magnitude of climate-driven variability of the Southern Ocean CO2 sink from observation-based air-sea O-2 fluxes. On interannual time scales, the variability in the air-sea fluxes of CO2 and O-2 estimated from observations is consistent across the two species and positively correlated with the variability simulated by ocean models. Our analysis suggests that variations in ocean ventilation related to the Southern Annular Mode are responsible for this interannual variability. On decadal time scales, the existence of significant variability in the air-sea CO2 flux estimated from observations also tends to be supported by observation-based estimates of O-2 flux variability. However, the large decadal variability in air-sea CO2 flux is absent from ocean models. Our analysis suggests that issues in representing the balance between the thermal and non-thermal components of the CO2 sink and/or insufficient variability in mode water formation might contribute to the lack of decadal variability in the current generation of ocean models.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'.