  This is a review on structure of the fermion mass terms in quantum field
theory, under the perspective of its practical applications in the real physics
of Nature -- specifically, we discuss fermion mass structure in the Standard
Model of high energy physics, which successfully describes fundamental physics
up to the TeV scale. The review is meant to be pedagogical, with detailed
mathematics presented beyond the level one can find any easily in the
textbooks. The discussions, however, bring up important subtleties and
ambiguities about the subject that may be less than well appreciated. In fact,
the naive perspective of the nature and masses of fermions as one would easily
drawn from the presentations of fermion fields and their equations of motion
from a typical textbook on quantum field theory leads to some confusing or even
wrong statements which we clarify here. In particular, we illustrate clearly
that a Dirac fermion mass eigenstate is mathematically equivalent to two
degenerated Majorana fermion mass eigenstates at least so long as the mass
terms are concerned. There are further ambiguities and subtleties in the exact
description of the eigenstate(s). Especially, for the case of neutrinos, the
use of the Dirac or Majorana terminology may be mostly a matter of choice. The
common usage of such terminology is rather based on the broken $SU(2)$ charges
of the related Weyl spinors hence conventional and may not be unambiguously
extended to cover more complicate models.
