The quantum reality problem is that of finding a mathematically precise definition of a sample space of configurations of beables, events, histories, paths, or other mathematical objects, and a corresponding probability distribution, for any given closed quantum system. Given a solution, we can postulate that physical reality is described by one randomly chosen configuration drawn from the sample space. For a physically sensible solution, this postulate should imply quasiclassical physics in realistic models. In particular, it should imply the validity of Copenhagen quantum theory and classical dynamics in their respective domains. A Lorentzian solution applies to relativistic quantum theory or quantum field theory in Minkowski space and is defined in a way that respects Lorentz symmetry. We outline a solution to the nonrelativistic and Lorentzian quantum reality problems and associated generalizations of quantum theory.