Abstract: I will review the classic paper "Clifford modules", by Atiyah, Bott, and Shapiro, which had its 50th birthday last month. This paper explores both Clifford algebras and K-theory, and the connections between them. In particular, we see that Bott periodicity arises as a purely algebraic phenomenon in the study of Clifford modules. Although this paper did not give a proof of Bott periodicity in K-theory via Clifford algebras, it certainly provided strong evidence in that direction. (This problem was tackled by other authors at the same time.) Time permitting, I will discuss some of the topological applications that arise from applying the algebraic machinery of Clifford modules to K-theory, such as the Thom isomorphism and vector fields on spheres.