Long-term observations have shown that black hole X-ray binaries exhibit strong, aperiodic variability on time scales of a few milliseconds to seconds. In addition, these systems also exhibit rapid variability in their X-ray light curves termed quasi-periodic oscillations (QPOs); also broadly classified into high-frequency and low-frequency QPOs. Understanding the nature of these variabilities and the underlying physical processes helps us probe the nature of the compact object and its surroundings. In this talk, I will begin by providing an overview of the existing theoretical models for broadband variability and various types of QPOs. I will then highlight findings from the latest state-of-the-art simulations of accretion discs that aim to reproduce these time variability phenomena. In particular, I will discuss how the fluctuations in the mass accretion rate, driven by the turbulence in the simulations, naturally account for the observed broad-band variability in the accreting systems, as well as the viability of the relativistic precession model in explaining low-frequency QPOs. Finally, I will briefly discuss the direct comparison of these results with current polarization missions such as IXPE and XPoSat.