The color gamut supported by current commercial displays is only a subset of the full spectrum of colors visible by the human eye. In High-Definition (HD) television technology, the scope of the supported colors covers 35.9% of the full visible gamut. For comparison, Ultra High-Definition (UHD) television, which is currently being deployed on the market, extends this range to 75.8%. However, when reproducing content with a wider color gamut than that of a television, typically UHD content on HD television, some original color information may lie outside the reproduction capabilities of the television. Efficient gamut mapping techniques are required in order to fit the colors of any source content into the gamut of a given display. The goal of gamut mapping is to minimize the distortion, in terms of perceptual quality, when converting video from one color gamut to another. It is assumed that the efficiency of gamut mapping depends on the color space in which it is computed. In this article, we evaluate 14 gamut mapping techniques, 12 combinations of two projection methods across six color spaces as well as R'G'B Clipping and wrong gamut interpretation. Objective results, using the CIEDE2000 metric, show that the R'G'B Clipping is slightly outperformed by only one combination of color space and projection method. However, analysis of images shows that R'G'B Clipping can result in loss of contrast in highly saturated images, greatly impairing the quality of the mapped image.