Abstract: In 1997, a long-standing mystery was solved when it was determined that cosmic gamma-ray bursts originate in distant galaxies whose redshifts are as great as 2 or more. Until then, it was not clear that these brief flashes of gamma radiation were not originating in our own galaxy. With their cosmological origin established, gamma-ray bursts are the most powerful electromagnetic explosions in the universe, liberating 10^52 erg of energy. But numerous mysteries remain. The origin of the energy is not known - it could be merging neutron stars, or hypernovae. Also, the origin of certain sub-classes of bursts is not clear. They could conceivably originate at closer distances. In the course of studying gamma-ray bursts, we have discovered another type of transient source, the soft gamma repeaters. These are indeed galactic neutron stars, and we have good evidence that they posess magnetic fields of 10^14 G and higher. I will review the data and theories of both objects in this talk.