Complementary colors have long been thought important to color vision due to their ability (as admixed pairs) to extinguish all chromaticity, and to adapt automatically (i.e., wavelength pairs and radiant power ratios) to illuminant. Their role in color mixture and chromatic induction is well documented but other roles have not been demonstrated. This article studies the structure of complementary colors in the wavelength and radiance dimensions over the hue cycle (the nonspectrals are represented by a nominal-wavelength metric). In the wavelength dimension, the basic structure of complementary colors is the complementary intervals ratio (ratio of a wavelength interval to its complementary interval of 1 nm). The ratio has RGB peaks, complementary CMY troughs, and provides models of chromatic induction, wavelength discrimination, and uniform hue difference in good agreement with data. Novel analyses of six color order/UCS hue circles indicate essential characteristics of a uniform hue scale. In the radiance dimension, basic structure is the complementary powers ratio (power of a stimulus required to neutralize its complementary of 1 Watt). The inverse structure has RGB peaks, complementary CMY troughs, and provides models of saturation, spectral sensitivity, and chromatic adaptation to illuminant. The RGB peaks demonstrate spectral sharpening, implying a postreceptoral location in the physiology. The models indicate that complementary colors have a significant role in color appearance besides their well known role in color mixture. (C) 2009 Wiley Periodicals, Inc. Col Res Appl, 34 233-252, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20490