  The depth of our theoretical understanding of neutrino flavor mixing should
match the importance of this phenomenon as a herald of long-awaited empirical
challenges to the standard model of particle physics. After reviewing the
familiar, simplified quantum mechanical model and its flaws, I sketch the
deeper understanding of both vacuum and matter-enhanced flavor mixing that is
found in the framework of scattering theory. While the simplified model gives
the ``correct answer'' for atmospheric, solar, and accelerator/reactor neutrino
phenomena, I argue that a key insight from the deeper picture will simplify the
treatment of neutrino transport in astrophysical environments---supernovae, for
example---in which neutrinos play a dynamically important role.
