Plants take up atmospheric CO2 through photosynthesis, and release CO2 back to the atmosphere during respiration. Since plants generally take up more CO2 than they release, they act as a net sink of carbon. The rates of photosynthesis and respiration, and therefore the ability of plants to store carbon, are sensitive to atmospheric CO2 concentration. However, the sensitivity of photosynthesis and respiration to CO2 concentrations is not yet well-constrained over geological time, over a wide range of CO2 and O2 concentrations. This sensitivity also affects fractionation of carbon isotopes during photosynthesis. The uncertainty presents an underrecognized problem, but also an opportunity for interesting new research directions, because the stable carbon isotope compositions of ancient plants and fossil animals are routinely used to place constraints on past CO2 concentrations, plant water-use efficiency, and the carbon cycle. Recent studies have improved the picture: CO2 concentrations have a clear effect on the carbon isotopic composition of most of the terrestrial biosphere (C3-type plants), with variation between C3 plant groups, and also in response to atmospheric O2 concentrations. An overview of this subject is presented, along with recent developments, and implications for studies of past atmospheric composition.