The present climate of Venus is controlled by an efficient carbon dioxide-water greenhouse effect and by the radiative properties of its global cloud cover. Both the greenhouse effect and clouds are sensitive to perturbations in the abundance of atmospheric water vapor and sulfur gases. Planetary-scale processes involving the release, transport, and sequestering of volatiles affect these abundances over time, driving changes in climate. We have developed a numerical model of the climate evolution of Venus. Atmospheric temperatures are calculated using a one-dimensional two-stream radiative-convective model that treats the transport of thermal infrared radiation in the atmosphere and clouds. These radiative transfer calculations are the first to utilize high-temperature, high-resolution spectral databases for the calculation of infrared absorption and scattering in Venus' atmosphere. We use a chemical/microphysical model of Venus' clouds to calculate changes in cloud structure that result from variations in atmospheric water and sulfur dioxide. Atmospheric abundances of water, sulfur dioxide, and carbon dioxide change under the influence of the exospheric escape of hydrogen, outgassing from the interior, and heterogeneous reactions with surface minerals. Radar images from the Magellan mission show that the surface of Venus has been geologically active on a global scale, yet its sparse impact cratering record is almost pristine. This geologic record on Venus is consistent with an epoch of rapid plains emplacement 600-1100 Myr ago. Our models show that intense volcanic outgassing of sulfur dioxide and water during this time would have resulted in the formation of massive sulfuric acid/water clouds and the cooling of the surface for 100-300 Myr. The thick clouds would have subsequently given way to high, thin water clouds as atmospheric sulfur dioxide was lost to reactions with the surface. Surface temperatures approaching 900 K would have been reached 200-500 Myr after the onset of volcanic resurfacing. Evolution to current conditions would have proceeded due to loss of atmospheric water at the top of the atmosphere, ongoing low-level volcanism, and the reappearance of sulfuric acid/water clouds. We find that the maintenance of sulfuric acid/water clouds on Venus today requires sources of outgassed sulfur active in the past 20-50 Myr, in contrast with the 1.9 Myr as determined from geochemical arguments alone (B. Fegley and R. G. Prinn 1989, Nature337, 55-58).