Over a decade ago, a group of supernova explosions with peak luminosities far exceeding (often by >100 times) those of normal events has been identified. These superluminous supernovae (SLSNe) have been a focus of intensive study. I review the accumulated observations and discuss the implications for the physics of these extreme explosions. SLSNe can be classified into hydrogen-poor (SLSNe-I) and hydrogen-rich (SLSNe-II) events. Combining photometric and spectroscopic analysis of samples of nearby SLSNe-I and lower-luminosity events, a threshold of mag at peak appears to separate SLSNe-I from the normal population. SLSN-I light curves can be quite complex, presenting both early bumps and late postpeak undulations. SLSNe-I spectroscopically evolve from an early hot photospheric phase with a blue continuum and weak absorption lines, through a cool photospheric phase resembling spectra of SNe Ic, and into the late nebular phase. SLSNe-II are not nearly as well studied, lacking information based on large-sample studies. Proposed models for the SLSN power source are challenged to explain all the observations. SLSNe arise from massive progenitors, with some events associated with very massive stars ( M). Host galaxies of SLSNe in the nearby Universe tend to have low mass and subsolar metallicity. SLSNe are rare, with rates <100 times lower than ordinary supernovae. SLSN cosmology and their use as beacons to study the high-redshift Universe offer exciting prospects.