Throughout Earth's history, the oceans have played a dominant role in the climate system through the storage and transport of heat and the exchange of water and climate-relevant gases with the atmosphere. The ocean's heat capacity is approximately 1,000 times larger than that of the atmosphere, its content of reactive carbon more than 60 times larger. Through a variety of physical, chemical, and biological processes, the ocean acts as a driver of climate variability on time scales ranging from seasonal to interannual to decadal to glacial-interglacial. The same processes will also be involved in future responses of the ocean to global change. Here we assess the responses of the seawater carbonate system and of the ocean's physical and biological carbon pumps to (i) ocean warming and the associated changes in vertical mixing and overturning circulation, and (ii) ocean acidification and carbonation. Our analysis underscores that many of these responses have the potential for significant feedback to the climate system. Because several of the underlying processes are interlinked and nonlinear, the sign and magnitude of the ocean's carbon cycle feedback to climate change is yet unknown. Understanding these processes and their sensitivities to global change will be crucial to our ability to project future climate change.