Chapter 1 provides an outline of the mathematical foundations of diffusion processes as models of Brownian motion in physics and the origins of diffusion models of decision making in psychology, along with their recent applications in disciplines like neuroscience and economics. The models assume that decisions are made by accumulating noisy evidence to decision criteria and provide a unified account of psychology’s two fundamental dependent variables of accuracy and response time. The chapter describes the origins of the models in efforts to understand why the speed and accuracy of decision making is inherently variable from one decision to the next. Contemporary diffusion models are the culmination of a body of theoretical development that extends back through the sequential-sampling models of the 1960s, signal detection theory, Wald’s sequential statistics, Thurstone’s law of comparative judgment, to Fechner’s study of just noticeable differences in the mid-nineteenth century. The chapter concludes with a summary of the organization of the book.