One of the most important natural mechanisms for carbon sequestration on our planet involves oceanic processes. Photosynthetic microbes convert inorganic carbon sources into living carbon forms that are the primary food source in the ocean. This organic carbon is transformed by organisms and transported by the dynamic ocean from the surface to varying depths, where it can remain for time periods ranging from days to hundreds of years. In this talk, I will describe how a combination of field studies, simple theories, and computations, allow us to probe two mechanisms that drive this process — 1. Sinking of particles, and their concomitant re-mineralization which determines the extent and efficiency of carbon export. We find that incorporating the known diversity of particle size and form into a minimal model generates the observed exponential or power-law profile of particulate sinking flux. — 2. Advection by oceanic flows, which we measure using observations from expeditions in the North Atlantic and Mediterranean Sea. We find that three-dimensional coherent flow pathways convey carbon from the chlorophyll maximum (in the upper 50 m) to the mesopelagic layer (100- 600 m depth) of the ocean. Observations and theoretical estimates confirm that this advective transport results in a significant downward flux of microbial carbon. Taken together, these mechanisms account for a large fraction of the biological carbon pump. I will conclude by discussing how these processes may change in a future climate and challenges for geoengineering them.