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Published online by Cambridge University Press: 25 May 2016
I describe the evidence that Soft Gamma Repeaters are magnetars—neutron stars in which a decaying magnetic field (rather than rotation) is the dominant source of free energy. The focus here is on the bursting emission of these sources and on direct physical diagnostics of very strong magnetic fields (B ≳ 10 BQED = 4.4 × 1014 G). I also summarize the trapped fireball model of SGR outbursts, the influence of QED processes on their spectra and lightcurves, and the genetic connection between neutron star magnetism and the violent fluid motions in a collapsing supernova core.