Ultra-luminous X-ray sources (ULXs) are extragalactic, off-nuclear X-ray sources with luminosities exceeding the Eddington limit for accretion onto stellar-mass compact objects. Their extreme luminosities, reaching several to over a hundred times the Eddington luminosity, initially motivated interpretations invoking intermediate-mass black holes accreting at sub-Eddington rates. However, subsequent observations and theoretical developments have favoured an alternative picture in which ULXs are powered by stellar-mass compact objects accreting at super-Eddington rates. A major breakthrough came with the discovery of coherent X-ray pulsations from several ULXs, unambiguously establishing neutron stars as the accretors in a subset of these sources and further supporting the super-Eddington accretion scenario onto stellar-mass compact objects. X-ray spectral studies reveal features such as high-energy curvature, soft excess emission, and ionized absorption or emission lines tracing powerful winds, while timing analyses, ranging from variability studies to pulsation detection, provide key constraints on the accretion geometry and emission mechanisms in these sources.

In this presentation, I will outline our efforts to better understand the accretion processes and the environments of ULXs. The work started with a comparative study of the broadband spectra of ultra-luminous X-ray pulsars (ULXPs) and Galactic accretion-powered X-ray pulsars, including sources in the Magellanic Clouds, followed by an investigation of possible signatures of X-ray reprocessing in ULXs through iron line searches, hardness-ratio studies during the eclipse transitions, and eclipse to out-of-eclipse flux ratio measurements in the eclipsing ULXs.  Additionally, we investigated variability and pulse-profile properties in selected ULXs and ULXPs. Finally, I will briefly present my learning experience and contributions to the development and calibration of the POLIX, an X-ray polarimeter instrument.