If the neutrino mass ordering turns out to be inverted, one may always reorder it to be normal. In this case the resulting pattern of the PMNS matrix looks strange and needs an explanation. Given the normal neutrino mass ordering, on the other hand, one is usually concerned about how small the effective Majorana mass term of a neutrinoless double-beta decay can be. In this seminar I will address both issues by presenting some new phenomenological observations, and discuss a possible connection between the mu-tau reflection symmetry breaking and the neutrino mass ordering, octant of theta(23) and CP violation.