Many contemporary studies of lightness perception are guided by a basic theoretical model in which lightness is computed in three stages involving: 1) extraction of the edge contrast or luminance ratios at the locations of luminance borders within the image; 2) spatial integration of the border signals to establish a scale of relative lightness values for the regions lying between borders; and 3) anchoring of the relative lightness scale to a physical referent (commonly assumed to be the highest luminance in the scene) in order to produce an absolute lightness scale. One important implication of this theory is that the lightnesses of regions lying between borders are perceptually filled in by the brain. I will review some key findings that support this basic scheme for computing lightness and then describe a specific computational model of lightness processing that I have developed to account for quantitative lightness matching data gathered collected in our lab. A key assumption of the model is that achromatic color is computed from a linear combination of lightness and darkness induction signals that spread spatially from borders and decay with distance. The model makes strong quantitative predictions that have so far been verified by the psychophysical tests and it establishes a theoretical bridge between the results of these lightness matching experiments and measures of sensory magnitude based on Stevens' magnitude estimation technique.