A diverse range of physical processes are responsible for regulating star formation across galaxies. Understanding their relative contributions to galaxy growth and quenching at different epochs is one of the key questions in galaxy evolution today. Since the processes driving galaxy growth, quenching and morphological transformations are thought to have characteristic timescales, studying the strength of stochastic star formation rate (SFR) fluctuations on these timescales allows us to disentangle their relative contributions for a population of galaxies. In this talk, I will give a brief summary of current work focusing on (i) establishing a formalism to study the stochasticity of star formation at a given time-scale and analyzing a variety of cosmological galaxy evolution simulations using this formalism, and (ii) observational methods of reconstructing star formation histories, which yield constraints on the time-scales of galaxy growth, morphological transformations, and quenching. Taken together, simulations and observations leverage predictive power against observational constraints, allowing us to develop a fuller picture of how galaxies evolve over time.