  Ultraluminous X-ray sources (ULXs) are amongst the most intriguing of X-ray
source classes. Their extreme luminosities - greater than 10^39 erg/s in the
0.3 - 10 keV band alone - suggest either the presence of black holes larger
than those regularly encountered in our own Galaxy (the Galactic centre
excepted), or sources apparently radiating well above the Eddington limit. We
review the insights afforded us by studies of their X-ray emission, focussing
on what this reveals about the underlying compact object. In particular, we
discuss recent deep observations of ULXs by the XMM-Newton observatory, and how
the unprecedented data quality provided by this mission is starting to
discriminate between the different physical models for these extraordinary
X-ray emitters.
