We review the current understanding of the temperature responses of C3 and C4 photosynthesis across thermal ranges that do not harm the photosynthetic apparatus. In C3 species, photosynthesis is classically considered to be limited by the capacities of ribulose 1·5-bisphosphate carboxylase/oxygenase (Rubisco), ribulose bisphosphate (RuBP) regeneration or Pi regeneration. Using both theoretical and empirical evidence, we describe the temperature response of instantaneous net CO2 assimilation rate (A) in terms of these limitations, and evaluate possible limitations on A at elevated temperatures arising from heat-induced lability of Rubisco activase. In C3 plants, Rubisco capacity is the predominant limitation on A across a wide range of temperatures at low CO2 (<300 µbar), while at elevated CO2, the limitation shifts to Pi regeneration capacity at suboptimal temperatures, and either electron transport capacity or Rubisco activase capacity at supraoptimal temperatures. In C4 plants, Rubisco capacity limits A below 20 °C in chilling-tolerant species, but the control over A at elevated temperature remains uncertain. Acclimation of C3 photosynthesis to suboptimal growth temperature is commonly associated with a disproportional enhancement of the Pi regeneration capacity. Above the thermal optimum, acclimation of A to increasing growth temperature is associated with increased electron transport capacity and/or greater heat stability of Rubisco activase. In many C4 species from warm habitats, acclimation to cooler growth conditions increases levels of Rubisco and C4 cycle enzymes which then enhance A below the thermal optimum. By contrast, few C4 species adapted to cooler habitats increase Rubisco content during acclimation to reduced growth temperature; as a result, A changes little at suboptimal temperatures. Global change is likely to cause a widespread shift in patterns of photosynthetic limitation in higher plants. Limitations in electron transport and Rubisco activase capacity should be more common in the warmer, high CO2 conditions expected by the end of the century.