  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.
