The $\mu$-$\tau$ reflection symmetry of Majorana neutrinos

The observed pattern of lepton flavor mixing and CP violation strongly indicates the possible existence of a simple flavor symmetry in the neutrino sector -- the effective Majorana neutrino mass term keeps invariant when the three left-handed neutrino fields transform as $\nu^{}_{e \rm L} \to (\nu^{}_{e \rm L})^c$, $\nu^{}_{\mu \rm L} \to (\nu^{}_{\tau \rm L})^c$ and $\nu^{}_{\tau \rm L} \to (\nu^{}_{\mu \rm L})^c$. A direct application of such a $\mu$-$\tau$ reflection symmetry to the canonical seesaw mechanism can help a lot to constrain the flavor textures of active and sterile Majorana neutrinos. The present article is intended to summarize the latest progress made in exploring the properties of this minimal flavor symmetry, its translational and rotational extensions, its soft breaking effects via radiative corrections from a superhigh energy scale to the electroweak scale, and its various phenomenological implications.