In recent years, we have been working on reconciling models of marine primary production with photo-acclimation models that deal with the relationship between phytoplankton carbon and chlorophyll concentration. In this paper, I will present our recent findings in the theoretical developments. I will also discuss how we have used these models in conjunction with satellite ocean-colour products from the Ocean Colour Climate Change Initiative of the European Space Agency to generate a long time series of primary production and phytoplankton carbon at the global scale. The work also incorporates a model of Brewin and colleagues to partition the phytoplankton carbon into three size classes. There are gaps in our knowledge that have to be addressed to make further progress. These include paucity of data on the maximum chlorophyll-to-carbon ratio that phytoplankton reach at light levels approaching zero, and the variability of this ratio with phytoplankton type. Another gap in our knowledge is related to the differences in the time scales of primary production and photo-acclimation. The work was supported by the BICEP Project of ESA and the CBIOMES project of the Simons Foundation. I gratefully acknowledge the work of many colleagues, who worked with me and contributed in various ways to this work, especially Trevor Platt.