Supernovae (SNe), the luminous explosions of stars, were observed since antiquity, with typical peak luminosity not exceeding 1.2x10^{43} erg/s (absolute magnitude >-19.5 mag). It is only in the last dozen years that numerous examples of SNe that are substantially super-luminous (>7x10^{43} erg/s; <-21 mag absolute) were well-documented. Reviewing the accumulated evidence, we define three broad classes of super-luminous SN events (SLSNe). Hydrogen-rich events (SLSN-II) radiate photons diffusing out from thick hydrogen layers where they have been deposited by strong shocks, and often show signs of interaction with circumstellar material. SLSN-R, a rare class of hydrogen-poor events, are powered by very large amounts of radioactive 56Ni and arguably result from explosions of very massive stars due to the pair instability. A third, distinct group of hydrogen-poor events emits photons from rapidly-expanding hydrogen-poor material distributed over large radii, and are not powered by radioactivity (SLSN-I). These may be the hydrogen-poor analogs of SLSN-II.
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