Ultraluminous X-ray sources (ULXs) are accreting black holes that may contain the missing population of intermediate mass black holes or reflect super-Eddington accretion physics. Ten years of Chandra and XMM-Newton observations of ULXs, integrated by multiband studies of their counterparts, have produced a wealth of observational data and phenomenological classifications. We review the properties of their host galaxies, list popular spectral models and implications for standard and supercritical accretion physics, demonstrate how X-ray timing of these objects places constraints on their masses. We also review multiwavelength studies of ULXs, including the optical emission of the binary system and nebulosity around them. We summarize that three classes of black holes could power ULXs: normal stellar mass black holes (∼10 M ⊙), massive stellar black holes (≲100 M ⊙), and intermediate mass black holes (10 2–10 4 M ⊙). We collect evidence for the presence of these three types of compact objects, including caveat of each interpretation, and briefly review their formation processes.