Globally, photosynthesis accounts for the largest flux of CO2 from the atmosphere into ecosystems and is the driving process for terrestrial ecosystem function. The importance of accurate predictions of photosynthesis over a range of plant growth conditions led to the development of a C3 photosynthesis model by Farquhar, von Caemmerer & Berry that has become increasingly important as society places greater pressures on vegetation. The photosynthesis model has played a major role in defining the path towards scientific understanding of photosynthetic carbon uptake and the role of photosynthesis on regulating the earth's climate and biogeochemical systems. In this review, we summarize the photosynthesis model, including its continued development and applications. We also review the implications these developments have on quantifying photosynthesis at a wide range of spatial and temporal scales, and discuss the model's role in determining photosynthetic responses to changes in environmental conditions. Finally, the review includes a discussion of the larger-scale modelling and remote-sensing applications that rely on the leaf photosynthesis model and are likely to open new scientific avenues to address the increasing challenges to plant productivity over the next century.