  Given its briefness and predictability, the minimal seesaw -- a simplified
version of the canonical seesaw mechanism with only two right-handed neutrino
fields -- has been studied in depth and from many perspectives, and now it is
being pushed close to a position of directly facing experimental tests. This
article is intended to provide an up-to-date review of various phenomenological
aspects of the minimal seesaw and its associated leptogenesis mechanism in
neutrino physics and cosmology. Our focus is on possible flavor structures of
such benchmark seesaw and leptogenesis scenarios and confronting their
predictions with current neutrino oscillation data and cosmological
observations. In this connection particular attention will be paid to the
topics of lepton number violation, lepton flavor violation, discrete flavor
symmetries, CP violation and antimatter of the Universe.
