Wind is an important driver of large-scale ocean currents, imparting momentum into the ocean at the sea surface. In particular, strong westerly winds help to drive the Antarctic Circumpolar Current, which of key importance for the global climate system. Over the past decades observations established that the strength of the westerlies over the Southern Ocean has increased as a result of climate change forcing. This increase is consistent with global climate model simulations. The future climate state depends strongly on how will the Antarctic Circumpolar Current respond to this strengthening. Eddy saturation is a theoretical regime where the transport of the current remains insensitive to the strengthening of the westerlies. Instead, the strengthening of the westerlies energizes transient eddies. Both satellite observations and numerical simulations suggest that the Antarctic Circumpolar Current is close to the eddy saturated limit. Traditionally eddy saturation has been attributed to baroclinic processes, but recent work suggests that barotropic processes that involve, e.g., standing meanders of the Antarctic Circumpolar Current, can also be responsible for producing eddy-saturated states. Here, we discus the different physical entities of the“usual” baroclinic eddy saturation as well as the recent notion of barotropic eddy saturation. We assess the relative importance of barotropic and baroclinic processes in producing eddy-saturated states using numerical simulations of primitive equations in an idealized setup. Lastly, we discuss potential implications these processes have on global ocean modeling.