Removing the influence of illumination and camera characteristics on image colors is an important image enhancement problem. It is solved by applying computational color constancy methods, whose goal is to assure that colors of objects in the image remain relatively constant regardless of the illumination conditions in the scene. Many such methods have been proposed and they either try to mimic the human visual system's color constancy or simply to produce visually appealing results by various means. These methods can operate locally by changing the color of each pixel individually or globally by changing all pixels in the same way. When the image scene is lit by several illumination sources, the application of local instead of global methods provides better results. However, the computational cost of local methods is higher than for global methods. The global methods are best applied when there is uniform illumination, their accuracy is relatively easily measured and evaluated, and they are faster than local methods. The latter is the main reason why they are also implemented in most digital cameras. Although many local and global color constancy methods have been proposed, neither of them gives satisfactory results in all conditions. On the other hand, some of the methods that give better results than other methods are not always suitable for real-time applications. All this means that there is still much space for improvements in terms of accuracy, resulting image quality, and computational speed. Guided by this need for these improvements, in this thesis several local and global color constancy methods suited for cases where high computational speed or high accuracy is needed are proposed. These methods can be summarized as follows: • a fast local method for color constancy and brightness adjustment in non-uniform illumination based on the Retinex theory of color vision; • a fast global Retinex-based method for color constancy in uniform illumination; and • a highly accurate global learning-based method for color constancy in uniform illumination using simplified models of possible illumination values. Experimental results of all of the proposed methods are presented and discussed. The proposed local methods are shown to produce results of high quality faster then some other methods used for the same purpose. As for the proposed global methods, in most cases the learning-based ones outperform the majority of other state-of-the-art methods in terms of accuracy. The proposed low-level statistics-based methods outperform all other methods in terms of computational speed while also having a relatively high accuracy and being hardware-friendly.