Collapsing stellar cores and the early universe are fantastic engines for generating neutrinos, ghostlike
particles which interact with matter only through the aptly named weak interaction and gravitation. However, neutrinos can more than make up for these feeble interactions with huge numbers. They can even come to dominate the energetics and element synthesis in the early universe and supernovae. The way neutrinos interact with matter depends on which of three "flavors" they come in, i.e., electron, muon, or tau flavor. We therefore must determine how neutrino flavor changes as these particles move through their surroundings. The advent of supercomputers has allowed us to follow this process in places, like supernova cores, where the flavor states of the neutrinos determine how flavor changes. Yes, the process can be quite nonlinear, and the results are startling and unexpected. Neutrinos can undergo collective flavor oscillations, producing signatures akin to domain formation in familiar condensed systems like ferromagnets. These signatures, if detected, could give us insights into astrophysical processes, but also into as yet unmeasured fundamental particle physics issues like the neutrino mass hierarchy.