  Ultraluminous X-ray binaries have challenged our assumptions of extreme
accretion rates in X-ray binaries, and impact other subfields of astronomy,
such as cosmology, gravitational wave sources and supernov{\ae}. Our
understanding of ULXs has changed tremendously over the last 35 years, and we
now know that ULXs can be powered by accreting neutron stars as well as black
holes, and can be found in a wide range of stellar environments. In this
chapter, we introduce the observational techniques used to discover and
characterize ULXs, and discuss our current understanding of their unique
accretion physics and formation channels.
