Fast radio bursts (FRBs) are millisecond bursts of radio radiation at frequencies of about 1 GHz, recently discovered in pulsar surveys. They have not yet been definitively identified with any other astronomical object or phenomenon. The bursts are strongly dispersed, indicating passage through a high column density of low density plasma. The most economical interpretation is that this is the interglactic medium, indicating that FRB are at "cosmological" distances with redshifts in the range 0.3-1.3. Their inferred brightness temperatures are as high as 10 37 • K, implying coherent emission by "bunched" charges, as in radio pulsars. I review the astronomical sites, objects and emission processes that have been proposed as the origin of FRB, with particular attention to soft gamma repeaters (SGRs) and giant pulsar pulses.