Some of the strongest interactions between ecological and climatic processes concern phytoplankton. While the importance of phytoplankton ecology for the global carbon cycle is well established, the role of their evolution is much less so. Adaptation is of particular importance in predicting the system's response to climate change, since it will modulate the ecological response to environmental change. Recent global ocean circulation models account for phytoplankton ecology. Here we propose to refine the definition of ecological processes and to allow for adaptation of phytoplankton cell size and shape in such models, as well as in more strategic models for freshwater systems. Phytoplankton communities are size-structured, and ecological functioning depends strongly on cell size and shape. Furthermore, phytoplankton size will influence the effectiveness of the biological carbon pump, through which carbon is sequestered from the atmosphere into the ocean interior by cell sinking. In addition, phytoplankton dynamics and evolution depend on interactions with higher trophic levels in the pelagic food web and these ecological interactions are generally also size structured. All these properties are shared between marine and freshwater systems. Phytoplankton ecology will be modelled by accounting for physiological structure (cell size, shape, nutrient quota) of phytoplankton communities and the size structure of the entire food web. We will study a range of models covering spatial scales from the global ocean to lakes. Different theoretical issues will be tackled using models at different spatial and temporal scales. The models will be used to formulate quantitative, testable predictions, that will be put to the test in experimental setups (outdoor freshwater mesocosms) and by using ecological and genomic data from the Tara Oceans expedition. The overall theoretical issue to be addressed is: does adaptation accelerate or mitigate the impact of climate change on the global carbon cycle?