The lac operon has been key in the study of genetic regulation. Consisting of three structural genes and a regulatory domain, the lac operon controls the manufacture of lactose-digesting enzymes in E. coli bacteria. The mechanisms through which it is repressed and activated are standard and apply to many operons in other genetic settings. As a result, scientists believe understanding the lac operon will help to decipher how more complicated genetic regulatory systems behave. A large amount of quantitative data has been generated from the lac operon, a consequence of both its small size and tractability. A variety of mathematical models have been employed to examine this data. Here, we will investigate how bifurcation theory, reverse engineering, and Gillespie's stochastic simulation method have all been used to uncover some aspect of the lac operon. Conclusions drawn from the results of these models promise to reveal new information about this operon.