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) a simple bipolar neutrino system that initially consists of monoenergetic ν e and Formula: see text, (b) a homogeneous and isotropic neutrino gas with multiple neutrino/antineutrino species and continuous energy spectra, and (c) 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 and/or constraining fundamental neutrino properties, such as the neutrino mass hierarchy and θ 13 from a future observed supernova neutrino signal.