Particles with energies below the mean energy E 0 in relativistic shocked plasmas should assume an equilibrium energy distribution. This leads to a synchrotron spectrum F ν ∝ ν 1/3 up to approximately the critical frequency ν 0 of an electron with the energy E 0 . Application to GRBs implies that a burst with 10 −5 erg/cm 2 s of soft gamma-rays and hν 0 = 300 KeV should be about 18th magnitude in visible light and a few µJy at 1 GHz (less if self-absorbed).

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Gamma-ray burst statistics are best explained by a source population at cosmological distances, while spectroscopy and intensity histories of some individual bursts imply an origin on Galactic neutron stars. To resolve this inconsistency I suggest the presence of two populations, one at cosmological distances and the other Galactic. I build on ideas of Shemi and Piran (1990) and of Mészáros and Rees (1993) involving the interaction of fireball debris with surrounding clouds to explain the observed intensity histories in bursts at cosmological distances. The distances to the Galactic population are undetermined because they are too few to affect the statistics of intensity and direction; I explain them as resulting from magnetic reconnection in neutron star magnetospheres.

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There are several phenomenological similarities between Soft Gamma Repeaters and Fast Radio Bursts, including duty factors, time scales and repetition. The sudden release of magnetic energy in a neutron star magnetosphere, as in popular models of SGR, can meet the energy requirements of FRB but requires both the presence of magnetospheric plasma in order that dissipation occur in a transparent region and a mechanism for releasing much of that energy quickly. FRB sources and SGR are distinguished by long-lived (up to thousands of years) current-carrying coronal arches remaining from formation of the young neutron star, and their decay ends the phase of SGR/AXP/FRB activity even though "magnetar" fields may persist. Runaway increase in resistance when the current density exceeds a threshold releases magnetostatic energy in a sudden burst and produces high brightness GHz emission of FRB by a coherent process; SGR are produced when released energy thermalizes as an equlibrium pair plasma. Failures of some alternative FRB models and the non-detection of SGR 1806-20 at radio frequencies are discussed in appendices.

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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.