The Arctic Ocean is one of the fastest changing oceans, plays an important role in global carbon cycling and yet is a particularly challenging ocean to study. Hence, observations tend to be relatively sparse in both space and time. How the Arctic functions, geophysically, but also ecologically, can have significant consequences for the internal cycling of carbon, and subsequently influence carbon export, atmospheric CO2 uptake and food chain productivity. Here we assess the major carbon pools and associated processes, specifically summarizing the current knowledge of each of these processes in terms of data availability and ranges of rates and values for four geophysical Arctic Ocean domains originally described by Carmack & Wassmann (2006): inflow shelves, which are Pacific-influenced and Atlantic-influenced; interior, river-influenced shelves; and central basins. We attempt to bring together knowledge of the carbon cycle with the ecosystem within each of these different geophysical settings, in order to provide specialist information in a holistic context. We assess the current state of models and how they can be improved and/or used to provide assessments of the current and future functioning when observational data are limited or sparse. In doing so, we highlight potential links in the physical oceanographic regime, primary production and the flow of carbon within the ecosystem that will change in the future. Finally, we are able to highlight priority areas for research, taking a holistic pan-Arctic approach.