  We review the rich phenomena associated with neutrino flavor transformation
in the presence of neutrino self-coupling. Our exposition centers on three
collective neutrino oscillation scenarios: a simple bipolar neutrino system
that initially consists of mono-energetic electron neutrinos and antineutrinos;
a homogeneous and isotropic neutrino gas with multiple neutrino/antineutrino
species and continuous energy spectra; and a generic neutrino gas in an
anisotropic environment. We use each of these scenarios to illustrate key
facets of collective neutrino oscillations. We discuss the implications of
collective neutrino flavor oscillations for core collapse supernova physics and
for the prospects of obtaining fundamental neutrino properties, e.g., the
neutrino mass hierarchy and $\theta_{13}$ from a future observed supernova
neutrino signal.
