Gamut mapping is a very actual problem in today's color reproduction. For a target device, a gamut mapping algorithm establishes a correspondence between the out of gamut color and the color within the gamut, trying to preserve same color appearance with the original color when that color is rendered on the target device. This problem becomes more important with the increasing number of color reproduction devices and cross media image representation. This paper focuses on some issues related to gamut mapping. First, the optimization of the target gamut is discussed because it may reduce many of the gamut mapping problems by reducing the volume of the out of gamut colors. Second, the influence of the color space in which the gamut mapping performs is discussed and a linearization procedure for CIELAB space is proposed. Third, a short overview of the existing gamut mapping procedure is given.