Sparse approximation is a well-established theory, with a profound impact on the fields of signal and image processing. In this talk we start by presenting this model and its features, and then turn to describe two special cases of it – the convolutional sparse coding (CSC) and its multi-layered version (ML-CSC). Amazingly, as we will carefully show, ML-CSC provides a solid theoretical foundation to … deep-learning. Alongside this main message of bringing a theoretical backbone to deep-learning, another central message that will accompany us throughout the talk: Generative models for describing data sources enable a systematic way to design algorithms, while also providing a complete mechanism for a theoretical analysis of these algorithms’ performance. This talk is meant for newcomers to this field – no prior knowledge on sparse approximation is assumed.