  Matter effects modify the mixing and the effective masses of neutrinos in a
way which depends on the neutrino mass hierarchy. Consequently, for normal and
inverted hierarchies the oscillations and flavor conversion results are
different. Sensitivity to the mass hierarchy appears whenever the matter
effects on the 1-3 mixing and mass splitting become substantial. This happens
in supernovae in wide energy range and in the matter of the Earth. The Earth
density profile is a multi-layer medium where the resonance and parametric
enhancements of oscillations occur. The enhancement is realized in neutrino
(antineutrino) channels for the normal (inverted) mass hierarchy. Multi-megaton
scale under ice (water) atmospheric neutrino detectors with low energy
threshold can establish mass hierarchy with $(3 - 10) \sigma$ confidence level
in few years. The main challenges of these experiments are discussed and
various ways to improve sensitivity are outlined. In particular, inelasticity
measurements will allow to increase significance of the hierarchy
identification by $20 - 50 \%$ .
