Ultraluminous X-ray Sources (ULXs) are extragalactic, off-nuclear point-like sources with exceptionally high luminosities exceeding the Eddington luminosity. The nature of these energetic systems remains heavily debated. Such high luminosities are generally accepted to be due to accretion onto a compact object although a fraction of them could be rotationally-powered. The most widely accepted interpretation of the nature of these systems initially included stellar-mass black holes accreting at super-Eddington rates with anisotropic (beamed) emission or intermediate-mass black holes accreting at much lower sub-Eddington rates. With extensive studies, neutron stars accreting at super-Eddington rates were recently introduced as a power source for ULXs after discoveries of coherent pulsations, first from the ULX system M82 X-2 and shortly after followed by NGC 7793 P13 and many others which eventually contributed to a growing group of pulsating ULXs or PULXs. In this talk, I will briefly review the evolution of observational diagnostics on the nature of ULXs focusing on widely accepted theoretical considerations for the origin of their spectral and timing properties. I will then discuss the implications of different modes used to describe the characteristics of the system, dependent on whether they harbor a black hole or a neutron star as an accretor.

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