The marine carbonate chemistry system is the reactions and dynamic equilibria in seawater that involve dissolved carbon dioxide (CO2) and the deprotonated forms of carbonic acid, which are bicarbonate ions and carbonate ions. This system affects other marine biogeochemical cycles and ecosystems through its strong influence on seawater pH. Currently, a rapid chemical perturbation is being driven by the accumulation of anthropogenic CO2 in the ocean, which has taken up a significant fraction of the CO2 emitted to the atmosphere by fossil fuel burning, cement manufacture and land-use change since pre-industrial times. To predict the future consequences, it is first essential to be able to accurately measure the present state of the system, and to understand how it operates. To contribute to these goals, I have firstly made new developments to the measurement techniques for two key system variables, namely total alkalinity and the stable isotopic composition of dissolved inorganic carbon. Secondly, I have combined results from recent research cruises along a hydrographic transect in the Northeast Atlantic with historical datasets in order to quantify the rate at which anthropogenic CO2 has accumulated in the interior ocean over the past three decades, demonstrating that the regional accumulation rate is greater than the global average. I have used model output to assess uncertainties in these results that are caused by spatiotemporal heterogeneity in the distribution of observations. Thirdly, I have carried out a theoretical investigation into the influence of marine calcifying phytoplankton, like coccolithophores, on air-sea CO2 exchange. I have shown that these organisms can behave either as CO2 sources or sinks depending upon their relative rates of calcification and autotrophic production, their nutrient uptake stoichiometry, and local seawater conditions. Finally, I provide suggestions for developments to the work presented in this thesis that might help to overcome some challenges that are likely to face this field of research in the future.