A quiet methodological revolution, a modeling revolution, has occurred over the past several decades, almost without discussion. In contrast, the 20th century ended with contentious argument over the utility of null hypothesis significance testing (NHST) Keywords: mathematical models, statistical models, null hypothesis significance testing (NHST), Sir Ronald Fisher, teaching methodology A relatively silent methodological revolution has occurred over the past several decades, almost without discussion. Instead, null hypothesis significance testing (NHST) has received virtually all of the attention. Statistical and mathematical modeling-which subsume NHST-have developed into a powerful epistemological system, within which NHST plays an important though not expansive role. To most practicing researchers in psychology, as well as in most statistics and methodology textbooks, NHST is the primary epistemological system used to organize quantitative methods. Instead, researchers and textbook authors should be discussing how to create and compare behavioral models that are represented mathematically and evaluated statistically.Models are all around us, and the term model has many meanings. For example, I built model airplanes as a child. We see male and female fashion models in magazines. Psychologists study role models. These disparate concepts share in common that they are all simplifications of a complex reality. The airplane model does not fly, though its physical appearance matches one that does. The runway model epitomizes beauty and fashion. Role models engage in idealized (though perhaps unrealistic) behavior. In the same sense, our language is also a model. Speaking or writing creates a verbal instantiation of a complex reality. Our language can be nuanced and evocative, as when Elizabeth Barrett Browning wrote about love. Yet language has inherent limitations that necessarily simplify the complexity that it describes. For example, the word love must not have much precision, if I can simultaneously love barbecue, John Steinbeck, and my wife (although precision is added by context, of course). Clearly, language structures have both flexibility and limitations as models of the complicated reality they describe, and so do mathematical models, the topic of this article.What are mathematical models? To Neimark and Estes (1967, p. v), "a mathematical model is a set of assumptions together with implications drawn from them by mathematical reasoning." Why not just use verbal or conceptual models? Bjork (1973)