The consideration of quantitative data is often required to perform research in both the physical and social sciences and, as a result, researchers must at times include mathematical models in their studies in order to use the data in a meaningful way. The use of stochastic, or probabilistic, methods is particularly useful for those who are attempting to predict future phenomena; for example, an economist may wish to advise a corporation by forecasting long-term prices of the corporation's assets, and an ecologist may wish to predict the migration of animal populations between regions and its e ffect on local ecosystems. To our dismay, such problems involving many uncontrollable factors and an aspect of uncertainty cannot be easily solved with the "simple" mathematical models we learn in our introductory algebra and calculus courses. Instead, we require the use of probabilities and the utilization of data that change over time. In this article we will present the method of stochastic processes (particularly Markov chains) in general, aiming to provide a working knowledge of the theory behind the method to be used. We will then demonstrate the wide applicability of Markov chains by introducing the method to several relevant fields of study, namely topics in economics and biology.