The quantum Heisenberg manifolds (QHMs) are noncommutative manifolds constructed by M. Rieffel as strict deformation quantizations of Heisenberg manifolds. The QHMs give another important family of noncommutative manifolds along with noncommutative two-tori. In this talk, we first review noncommutative Yang-Mills theory on the QHMs based on the framework given by Connes and Rieffel, and then we discuss recent results of Yang-Mills connections with constant curvature on the QHMs. This is a joint work with Franz Luef and Judith Packer.operator-valued strong L^2-functions.