  Here we provide an overview of what is known, and what is not known, about an
interesting dynamical system known as the Kepler-Heisenberg problem. The main
idea is to pose a version of the classical Kepler problem of planetary motion,
but in a sub-Riemannian setting. The result is system which is surprisingly
rich and beautiful, mysterious in some ways but tame in others, offering a
substantial number of questions which seem non-trivial yet tractable.
