I will introduce the notion of a coarse dynamical system on an unbounded metric space. A coarse analogue of topological entropy can be defined for these systems that measures the divergence of orbits on the large scale and is invariant under coarse conjugacy. I will discuss some cases where the coarse entropy differs from Bowen’s noncompact topological entropy and some cases where they coincide, as well as work in progress on other coarse dynamical invariants. This is joint work with Michał Misiurewicz.