I describe complementary colors' physiology and functional roles in color vision, in a three-stage theory (receptor, opponent color, and complementary color stages). 40 specific roles include the complementary structuring of: S and L cones, opponent single cells, cardinal directions, hue cycle structure, hue constancy, trichromatic color mixture, additive/subtractive primaries, two unique hues, color mixture space, uniform hue difference, lightness-, saturation-, and wavelength/hue-discrimination, spectral sensitivity, chromatic adaptation, metamerism, chromatic induction, Helson-Judd effect, colored shadows, color rendering, warm-cool colors, brilliance, color harmony, Aristotle's flight of colors, white-black responsivity, Helmholtz-Kohlrausch effect, rainbows/halos/glories, dichromatism, spectral-sharpening, and trimodality of functions (RGB peaks, CMY troughs whose complementarism adapts functions to illuminant). The 40 specific roles fall into 3 general roles: color mixture, color constancy, and color perception. Complementarism evidently structures much of the visual process. Its physiology is evident in complementarism of cones, and opponent single cells in retina, LGN, and cortex. Genetics show our first cones were S and L, which are complementary in daylight D65, giving a standard white to aid chromatic adaptation. M cone later split from L to oppose the nonspectral (red and purple) hues mixed from S+L. Response curves and wavelength peaks of cones L, S, and (S+L), M, closely resemble, and lead to, those of opponent-color chromatic responses y, b, and r, g, a bimodal system whose summation gives spectral-sharpened trimodal complementarism (RGB peaks, CMY troughs). Spectral sharpening demands a post-receptoral, post-opponent-colors location, hence a third stage.