In the 1830's Simeon-Denis Poisson developed the distribution that bears his name, basing it on the binomial distribution. He used it to show how the inherent variance in jury decisions affected the inferences that could be made about the probability of conviction in French courts. In recent years there have been a number of examples in which researchers have either ignored or forgotten this inherent variance and how OR, in particular mathematical modeling, can be used to incorporate this variance in analyses. This paper deals for the most part with mathematical models of offender and system behavior, especially those based on the stochastic, or random aspects of criminal justice data. The topics addressed are criminal careers, incapacitation, recidivism, deterrence, population projections, and patterns in crime. Looking to the future, it can be foreseen that the need to develop better means of handling the streams of data. Mathematical models are one way of addressing them. It might also be expected that, although analytic models will continue to be developed to provide the insights into crime and justice problems, more efforts will be devoted to understanding the data by using maps and other graphical or pictorial techniques. The development of new analytic models might then be based on insights gained from being able to visually infer patterns in the data. 15 figures and 215 references