X-ray binary systems are fascinating objects in the Universe. Despite a relatively good knowledge of their basic emission mechanisms, we still lack a complete understanding of their time, energy, and luminosity dependence. AstroSat, India's first multi-wavelength mission, is well-suited for studying this class of objects due to its wideband and fast timing capabilities. In the first part of my talk, I will discuss AstroSat results from the study of the first Galactic Ultra-luminous X-ray pulsar, Swift J0243.6+6124, an extragalactic transient super-Eddington accretor, RX J0209.6-7427, accretion-powered millisecond X-ray pulsars such as SAX J1748.9-2021, SAX J1808.4-3658, and an X-ray burster, 4U 1636-536, showing thermonuclear burst oscillations. The last part of the talk will focus on the curious case of a black-hole candidate X-ray transient, Swift J1357.2-0933. This source has previously shown intense dips in the optical light curve, a phenomenon linked to the existence of a "unique toroidal structure" in the inner region of the disc, seen at a high inclination. In our recent work, we observed millihertz quasi-periodic X-ray oscillations with frequencies varying between 1-5 mHz which was never observed before in this source. I will discuss the physical implications of our observational results.