Marine phytoplankton are responsible for over 45% of annual global net primary production. Ocean warming is expected to drive massive reorganisation of phytoplankton communities, resulting in pole-ward range shifts and sharp declines in species diversity, particularly in the tropics. The impacts of warming on phytoplankton species depend critically on their physiological sensitivity to temperature change (characterised by the thermal tolerance curve) and the capacity for rapid evolutionary adaptation to extend the upper limits of thermal tolerance. I will discuss new experimental data from my laboratory that shows how differences in the temperature responses of photosynthesis and respiration establish physiological trade-offs that constrain the thermal tolerance of 18 species of marine phytoplankton, spanning cyanobacteria as well as the red and green super-families. I will then present data from a series of investigations using laboratory selection experiments, which demonstrate that the rapid evolution of elevated thermal tolerance is linked to adjustments in physiological traits that increase the efficiency of photosynthetic energy allocation to growth at high temperatures. I will finish by discussing results of a whole genome resequencing investigation coupled to one of our long-term evolution studies with the marine diatom Thalassiosira pseudonana, and the challenges of linking patterns of molecular evolution to adaptive shifts in physiological traits.