Much of the progress made in image processing in the past decades can be attributed to better modeling of image content and a wise deployment of these models in relevant applications. This path of models spans from the simple l₂-norm smoothness through robust, thus edge preserving, measures of smoothness (e.g. total variation), and until the very recent models that employ sparse and redundant representations. In this paper, we review the role of this recent model in image processing, its rationale, and models related to it. As it turns out, the field of image processing is one of the main beneficiaries from the recent progress made in the theory and practice of sparse and redundant representations. We discuss ways to employ these tools for various image-processing tasks and present several applications in which state-of-the-art results are obtained.