Gene expression is the fundamental biological process by which RNA and protein molecules are produced in a cell based on the information encoded in the DNA. The regulation of gene expression dictates which genes are expressed and when, which is crucial for cells to perform specific functions and adapt to changes in their environment. Single-cell experiments reveal that RNA production occurs in bursts whose size and timing is random.  Over the last thirty years, a plethora of mathematical models of stochastic gene expression have been developed in order to understand the origin of this noise. However, solving these models analytically becomes progressively more difficult as their complexity is increased. In this talk, I will show how many of these models can be solved using the queueing theory, which in turn can help us to solve the inverse problem of inferring the kinetics of gene expression from single-cell measurements of RNA numbers.