  Neutrino oscillations are examined under the broad requirements of
  Poincar\'e-invariant scattering theory in an S-matrix formulation.
  This approach can be consistently applied to theories with either field or
particle degrees of freedom. The goal of this paper is to use this general
framework to identify all of the unique physical properties of this problem
that lead to a simple oscillation formula. We discuss what is in principle
observable, and how many factors that are important in principle end up being
negligible in practice.
