Stochasticity is a ubiquitous feature of cellular processes such as gene expression that can give rise to phenotypic differences for genetically identical cells. Understanding how the underlying biochemical reactions give rise to variations in mRNA/protein levels is thus of fundamental importance to diverse cellular processes. Recent technological developments have enabled single-cell measurements of cellular macromolecules which can shed new light on processes underlying gene expression. Correspondingly, there is a need for the development of theoretical tools to quantitatively model stochastic gene expression and its consequences for cellular processes. In this dissertation, we address this need by developing general stochastic models of gene expression. By mapping the system to models analyzed in queueing theory, we derive analytical expressions for the noise in steady-state protein distributions. Furthermore, given that the underlying processes are intrinsically stochastic, cellular regulation must be designed to control the`noise' in order to adapt and respond to changing environments. Another focus of this dissertation is to develop and analyze stochastic models of post-transcription regulation. The analytical solutions of the models proposed provide insight into the effects of different mechanisms of regulation and the role of small RNAs in fine-tunning the noise in gene expression. The results derived can serve as building blocks for future studies focusing on regulation of stochastic gene expression. / Ph. D.