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This is a review on structure of the fermion mass terms in quantum fieldtheory, under the perspective of its practical applications in the real physicsof Nature -- specifically, we discuss fermion mass structure in the StandardModel of high energy physics, which successfully describes fundamental physicsup to the TeV scale. The review is meant to be pedagogical, with detailedmathematics presented beyond the level one can find any easily in thetextbooks. The discussions, however, bring up important subtleties andambiguities 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 easilydrawn from the presentations of fermion fields and their equations of motionfrom a typical textbook on quantum field theory leads to some confusing or evenwrong statements which we clarify here. In particular, we illustrate clearlythat a Dirac fermion mass eigenstate is mathematically equivalent to twodegenerated Majorana fermion mass eigenstates at least so long as the massterms are concerned. There are further ambiguities and subtleties in the exactdescription of the eigenstate(s). Especially, for the case of neutrinos, theuse of the Dirac or Majorana terminology may be mostly a matter of choice. Thecommon usage of such terminology is rather based on the broken $SU(2)$ chargesof the related Weyl spinors hence conventional and may not be unambiguouslyextended to cover more complicate models.

Ambiguities and Subtleties in Fermion Mass Terms in Practical Quantum Field Theory