In 1992, Richard Schwartz defined the "pentagram map", a discrete dynamical system on polygons in the (real) projective plane. Years later, it was shown to be (Liouville) integrable. In this talk, I will briefly introduce dynamical systems and integrability. Then, I will discuss my current research in generalizing the pentagram map to projective planes over a large class of (non-commutative) rings.