This dissertation investigates the general problem of reproducing color images on an off-set printing press using custom inks in any combination and number. Many mathematical and algorithmic challenges arise when printing with inks other than the standard process colors (cyan, magenta, yellow, and black), particularly as the number of inks increases. These challenges include the development of gamut mapping strategies, efficient ink selection strategies, and robust methods for computing color separations in situations that may be either overconstrained or underconstrained. In addition, the demands of high-quality color printing require an accurate physical model of the colors that result from overprinting multiple inks using halftoning, including the effects of trapping, dot gain, and the interreflection of light between ink layers. As we explore these issues, we present new algorithms and physical models that together comprise a system capable of choosing optimal inks for an image and generating the appropriate color separations. Finally, we present some printed examples demonstrating the promise of our techniques.