Long-term observations have shown that black hole X-ray binaries exhibit 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): broadly classified into high-frequency and low-frequency QPOs. Understanding the origin of these variabilities and the underlying physical processes helps us probe the nature of the compact object and its surroundings. In this talk, starting with a pedagogical introduction to the accretion discs, I shall give a broad overview of the existing theoretical models for broadband variability and different types of QPOs. I will then focus on the findings from the current state-of-art simulations of accretion discs in reproducing such time variability phenomena. In particular, I will discuss how the mass accretion rate fluctuations generated by the turbulence in the simulations naturally explain the observed broadband variability in the accreting systems and the viability of the relativistic precession model for the low-frequency QPO.