In this survey talk I will walk you through a decade of fascinating research activity on “sparse and redundant representations”. We will start with a classic image processing task of noise removal and use it as a platform for the introduction of data models in general, and sparsity and redundancy as specific forces in such models. The emerging model will be shown to lead to a series of key theoretical and numerical questions, which we will handle next. A key problem with the use of sparse and redundant representation modeling is the need for a sparsifying dictionary – we will discuss ways to obtain such a dictionary by learning from examples, and introduce the K-SVD algorithm. Then we will show how all these merge into a coherent theory that can be deployed successfully to various image processing applications.