Radial and axial segregation is investigated experimentally in polydisperse mixtures of granular materials rotated in a long, partly filled, horizontal cylinder. Radial segregation by size is observed in all polydisperse mixtures. Axial segregation, with smaller-size particles forming bands within bands of larger-size particles, is observed for mixtures of 3 sizes. In addition, bands in ternary mixtures oscillate axially under some conditions. It is observed that the surface flow speeds depend on the particle size, both in the mixed and segregated case. A simple microscopic model based solely on different frictional properties of three particles yields qualitatively similar results.