In this paper, we introduce an unsupervised learning approach to automatically discover, summarize, and manipulate artistic styles from large collections of paintings. Our method is based on archetypal analysis, which is an unsupervised learning technique akin to sparse coding with a geometric interpretation. When applied to deep image representations from a collection of artworks, it learns a dictionary of archetypal styles, which can be easily visualized. After training the model, the style of a new image, which is characterized by local statistics of deep visual features, is approximated by a sparse convex combination of archetypes. This enables us to interpret which archetypal styles are present in the input image, and in which proportion. Finally, our approach allows us to manipulate the coefficients of the latent archetypal decomposition, and achieve various special effects such as style enhancement, transfer, and interpolation between multiple archetypes.