  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.
