Responses of individual leaves to short-term changes in CO2 partial pressure have been relatively well studied. Whole-plant and plant community responses to elevated CO2 are less well understood and scaling up from leaves to canopies will be complicated if feedbacks at the small scale differ from feedbacks at the large scale. Mathematical models of leaf, canopy, and ecosystem processes are important tools in the study of effects on plants and ecosystems of global environmental change, and in particular increasing atmospheric CO2, and might be used to scale from leaves to canopies. Models are also important in assessing effects of the biosphere on the atmosphere. Presently, multilayer and big leaf models of canopy photosynthesis and energy exchange exist. Big leaf models - which are advocated here as being applicable to the evaluation of impacts of 'global change' on the biosphere - simplify much of the underlying leaf-level physics, physiology, and biochemistry, yet can retain the important features of plant-environment interactions with respect to leaf CO2 exchange processes and are able to make useful, quantitative predictions of canopy and community responses to environmental change. The basis of some big leaf models of photosynthesis, including a new model described herein, is that photosynthetic capacity and activity are scaled vertically within a canopy (by plants themselves) to match approximately the vertical profile of PPFD. The new big leaf model combines physically based models of leaf and canopy level transport processes with a biochemically based model of CO2 assimilation. Predictions made by the model are consistent with canopy CO2 exchange measurements, although a need exists for further testing of this and other canopy physiology models with independent measurements of canopy mass and energy exchange at the time scale of 1 h or less.