Over the course of my PhD, I developed the analytical capability to measure calcium isotopes at the University of Cambridge and analyzed calcium isotopes in a range of fluids and minerals in modern and past environments. After discussing my methodological development, I report my work in the glacial precursor to the Dead Sea. Here, the calcium isotope composition of aragonite varies synchronously with lake level fluctuations over the last 70,000 years. My numerically reconstructed lake calcium budget led me to conclude that 20,000 years ago, the Dead Sea was wetter than modern conditions, rather than colder and drier, as had previously been proposed. The primary focus of my PhD research was understanding the sedimentary sink for carbon. The formation of authigenic carbonate in marine sediments is caused by the microbial degradation of organic matter. I used pore fluid measurements and a numerical model to identify zones of authigenic carbonate precipitation. This knowledge was then combined with an understanding of the microbial processes that occur beneath the seafloor to determine the link between microbial activity and authigenic carbonate formation. Two processes, sulfate reduction and the anaerobic oxidation of methane were determined to be the main drivers of authigenic carbonate precipitation. In order to assess the importance of the carbon isotope signal imparted by each of the two identified processes, I created Artificial Neural Networks to predict the areal extent of authigenic carbonate precipitation and the dominant microbial process driving the precipitation. My ANNs identified that 37% of the modern seafloor is precipitating authigenic carbonate, which leads to a flux of 1.2*10^12 moles of carbon per year, of which 88% is due to the anaerobic oxidation of methane, and 12% is due to sulfate reduction. This represents 2-3% of the modern global carbon deposition, however I was able to show that this would be significantly higher in the geological past when ocean conditions were vastly different to how they are today. Finally, I conclude by proposing that some variations in the global carbon cycle in the past can be explored by linking marine calcium concentrations to authigenic carbonate formation and the flux of alkalinity from the seafloor.