We model color contrast sensitivity for Gabor patches as a function of spatial frequency, luminance and chromacity of the background, modulation direction in the color space and stimulus size. To fit the model parameters, we combine the data from five independent datasets, which let us make predictions for background luminance levels between 0.0002 cd/m² and 10 000 cd/m², and for spatial frequencies between 0.06 cpd and 32 cpd. The data are well-explained by two models: a model that encodes cone contrast and a model that encodes postreceptoral, opponent-color contrast. Our intention is to create practical models, which can well explain the detection performance for natural viewing in a wide range of conditions. As our models are fitted to the data spanning very large range of luminance, they can find applications in modeling visual performance for high dynamic range and augmented reality displays.