Despite its rich history as a topic of interdisciplinary scientific endeavor, recent work in granular matter is yielding many surprises. One of the fascinating puzzles in pattern formation of granular flows--- with important industrial applications--- is the tendency of granular materials to segregate. In this presentation, I will demonstrate a novel segregation pattern, named spontaneous stratification, arising in granular flows of mixtures. I will propose a mechanism to explain this phenomenon, and use a phenomenological continuum approach to offer further insight into the mechanism of stratification. I will also discuss the implications of oue results for radial and axial segregation in rotating cylinders and the motion of sand dunes.