Primary productivity of terrestrial vegetation is expected to increase under the influence of increasing atmospheric carbon dioxide concentrations ([CO2]). Depending on the fate of such additionally fixed carbon, this could lead to an increase in terrestrial carbon storage, and thus a net terrestrial sink of atmospheric carbon. Such a mechanism is generally believed to be the primary global driver behind the observed large net uptake of anthropogenic CO2 emissions by the biosphere. Mechanisms driving CO2 uptake in the Terrestrial Biosphere Models (TBMs) used to attribute and project terrestrial carbon sinks, including that from increased [CO2], remain in large parts unchanged since those models were conceived two decades ago. However, there exists a large body of new data and understanding providing an opportunity to update these models, and directing towards important topics for further research. In this review we highlight recent developments in understanding of the effects of elevated [CO2] on photosynthesis, and in particular on the fate of additionally fixed carbon within the plant with its implications for carbon turnover rates, on the regulation of photosynthesis in response to environmental limitations on in-plant carbon sinks, and on emergent ecosystem responses. We recommend possible avenues for model improvement and identify requirements for better data on core processes relevant to the understanding and modelling of the effect of increasing [CO2] on the global terrestrial carbon sink.