More advanced color management systems rely on the availability of the gamut description of a color reproduction device. The problem of calculating such a gamut description, however, has no definitive solution yet.In this paper we explain that several kinds of surfaces exist in colorant space, that map to the gamut boundaries in color space. The different kinds of gamut boundaries that should be taken into account do not only depend on the mathematical model that describes the color mixing behavior of the reproduction device, but also depend on the colorant domain (e.g. colorant limitation) and the number of colorants of the printer.The color gamut boundaries can be determined mathematically for any printer model and any number of inks. For some models however, such as the Neugebauer equations, most kinds of gamut boundaries can be described analytically.