  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.
