The process of gene expression has two seemingly opposite characteristics: it is highly regulated on one hand, but on the other hand it is inherently random, due to the low copy number of molecules involved. Recent advances in detection techniques allow for direct observations of stochastic molecular events in live cells, with single molecule sensitivity. Here we describe the main methods used for dynamic single molecule detection of mRNA and protein production in live cells. Random bursts of protein production were observed, as well as of mRNA production in some cases. In all experiments to date, bursts occur at random times and the number of molecules per burst is exponentially distributed. We discuss these results using a theoretical model which relates the dynamic process of protein production in bursts to the distribution of protein levels in a population of cells. We propose the gamma distribution as a useful tool for analysis of protein level distributions, both in and out of steady-state. This model can provide quantitative information on the dynamic parameters describing protein production based on measured distributions of protein levels in populations of cells, which are much easier to obtain than dynamic data.