Astrophysics of the Soft Gamma Repeaters and Anomalous X-Ray Pulsars

I summarize the recent advances in our understanding of the Soft Gamma Repeaters: in particular their spin behavior, persistent emission and hyper-Eddington outbursts. The giant flares on 5 March 1979 and 27 August 1998 provide compelling physical evidence for magnetic fields stronger than 10 B_{QED} = 4.4 x 10^{14} G, consistent with the rapid spindown detected in two of these sources. The persistent X-ray emission and variable spindown of the 6-12 s Anomalous X-ray Pulsars are compared and contrasted with those of the SGRs, and the case made for a close connection between the two types of sources. Their collective properties point to the existence of {\it magnetars}: neutron stars in which a decaying magnetic field (rather than accretion or rotation) is the dominant source of energy for radiative and particle emissions. Observational tests of the magnetar model are outlined, along with current ideas about the trigger of SGR outbursts, new evidence for the trapped fireball model, and the influence of QED processes on X-ray spectra and lightcurves. A critical examination is made of coherent radio emission from bursting strong-field neutron stars. I conclude with an overview of the genetic connection between neutron star magnetism and the violent fluid motions in a collapsing supernova core.