Compact object binaries represent extraordinary laboratories within the universe, characterized by some of the strongest gravitational regimes and interactions of high-temperature matter. X-ray observations of these systems offer valuable insights into their emission components, shedding light on the physical properties of compact objects owing to the proximity of the emission region to these objects. In this seminar, I will delve into some of the intriguing White Dwarf and Neutron Star binaries, exploring their spectral and timing properties. The initial segment of my presentation will focus on Nova Her 2021, renowned as one of the fastest-declining Novae in recent times. Using simultaneous X-ray and UV observations with AstroSat, we probe the rotation period and the spectral properties of the source as a function of the rotation of the white dwarf. Subsequently, I will delve into a peculiar persistent Neutron Star binary, GX 340+0, elucidating how its spectro-timing properties can provide invaluable insights into the evolution of the source. I will discuss the prospects of X-ray polarization observations of these sources and how they can reveal the insights into the geometry of the emission components.