Résumé : In this survey, we highlight the appealing features and challenges of Sparse Component Analysis (SCA) for blind source separation (BSS). SCA is a simple yet powerful framework to separate several sources from few sensors, even when the independence assumption is dropped. So far, SCA has been most successfully applied when the sources can be represented sparsely in a given basis, but many other potential uses of SCA remain unexplored. Among other challenging perspectives, we discuss how SCA could be used to exploit both the spatial diversity corresponding to the mixing process and the morphological diversity between sources to unmix even underdetermined convolutive mixtures. This raises several challenges, including the design of both provably good and numerically efficient algorithms for large-scale sparse approximation with overcomplete signal dictionaries.