We review observations of ultraluminous X-ray sources (ULXs). X-ray spectroscopic and timing studies of ULXs suggest a new accretion state distinct from those seen in Galactic stellar-mass black hole binaries. The detection of coherent pulsations indicates the presence of neutron-star accretors in three ULXs and therefore apparently super-Eddington luminosities. Optical and X-ray line profiles of ULXs and the properties of associated radio and optical nebulae suggest that ULXs produce powerful outflows, also indicative of super-Eddington accretion. We discuss models of super-Eddington accretion and their relation to the observed behaviors of ULXs. We review the evidence for intermediate mass black holes in ULXs. We consider the implications of ULXs for super-Eddington accretion in active galactic nuclei, heating of the early universe, and the origin of the black hole binary recently detected via gravitational waves.
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