The oceans play an important role in regulating atmospheric CO2 levels and the climate system. Since the beginning of the Industrial Revolution, the ocean has absorbed more than 25% of anthropogenic CO2 emissions, and the carbon sink is expected to grow over the next several centuries as atmospheric CO2 concentrations rise. Multiple ocean processes, however, affect the amount of anthropogenic carbon that the ocean absorbs from the atmosphere. This thesis combines Earth System Models (ESM) from the sixth phase Coupled Model Intercomparison Project (CMIP6) with an offline inverse biogeochemical model to answer a fundamental question: What mechanisms control the size of the ocean carbon sink in a warming climate?First, I use the CMIP6 models to investigate the role of meridional overturning circulation in ocean carbon uptake (Chapter 2). Slowing MOC reduces anthropogenic carbon uptake by the solubility pump while increasing deep ocean carbon and nutrient storage by the biological pump. The net effect is a reduction in the ocean carbon sink. I then used an offline inverse biogeochemical model to conduct a series of sensitivity experiments to better understand how changes in circulation affect the ocean carbon sink (Chapter 3). The results show that slowing MOC reduces anthropogenic carbon uptake by decreasing biological productivity. The slowing MOC sequesters more nutrients in the deep ocean, reducing nutrient replenishment to the upper ocean and thus lowering biological productivity. This increases ocean surface CO2 saturation and reduces the ocean's ability to absorb anthropogenic CO2 from the atmosphere. However, without taking into account changes in biological productivity, the slowing MOC contributes little to the ocean carbon sink. In Chapter 4, I examine the ocean ventilation timescales and patterns in a time-evolving circulation in the context of climate change. I found that slowing meridional overturning circulation causes a 110-year increase in global-averaged mean age from the year 1850 to 2300. However, where and when the water will be re-exposed to the atmosphere is highly dependent on the post-2300 circulation. The dependence of interior-to-surface transit time on future ocean circulation produces great uncertainties in the long-term durability of the ocean CDR strategies.