Prospects for Measurement of the Neutrino Mass Hierarchy

The unknown neutrino mass hierarchy -- whether the $\nu_3$ mass eigenstate is the heaviest or the lightest -- represents a major gap in our knowledge of neutrino properties. Determining the hierarchy is a critical step toward further precision measurements in the neutrino sector. The hierarchy is also central to interpreting the next generation of neutrinoless double beta decay results, plays a role in numerous cosmological and astrophysical questions, and serves as a powerful model discriminant for theories of neutrino mass generation and unification. Various current and planned experiments claim sensitivity for establishing the neutrino mass hierarchy. We review the most promising of these here, paying special attention to points of concern and consolidating the projected sensitivities into an outlook for the years ahead.