Abstract: The evolution of a quantum system is governed by its discrete energies. These energies are almost always assumed to be real, as is guaranteed by Hermiticity of the system Hamiltonian. I will present our recent experiments that explore the consequences of complex energies, allowing non-Hermitian dynamics, which include novel features arising from the topology of the Riemann manifolds that describe complex energies. The degeneracies that occur with these non-Hermitian Hamiltonians are known as exceptional points. Our observations demonstrate rich phenomena associated with non-Hermitian physics and exceptional points such as non-orthogonality of eigenstates in a fully quantum regime and open routes to explore and harness exceptional point degeneracies for enhanced sensing and quantum information processing.