Waiting in a queue (or a line) for some type of service is a commonplace experience. People do this at a grocery store, bank, amusement park or DMV, to give just a few examples. These customer service systems feature inherent randomness, which impacts performance. Modern computer and communications systems, manufacturing processes, transportation systems and even biological networks experience similar stochastic effects. Stochastic network theory is the study of the performance and optimal control of such systems. At the beginning of the talk, I will show a few simple examples of where mathematics plays an integral role in illuminating system behavior. Following that I will discuss some of the mathematical challenges associated with analyzing the performance of modern networks. \\ \\ Finally, I will end by discussing work-in- progress related to modern call centers that is joint with Amy Ward (U. Chicago Booth) and Yueyang Zhong (U. Chicago Booth).