Although dynamical systems have been used by cognitive scientists for more than a decade already (e.g. Kugler, Kelso, and Turvey, 1980), dynamical systems ?rst gained widespread attention in the mid-1990s (e.g. Kelso, 1995; Port and van Gelder, 1995; Thelen and Smith, 1994). Dynamical systems theory was then, and continues to be, a crucial tool for embodied cognitive science. The word dynamical simply means “changing over time” and thus a dynamical system is simply a system whose behavior evolves or changes over time. The scienti?c study of dynamical systems is concerned with understanding, modeling, and predicting the ways in which the behavior of a system changes over time. In the last few decades, thanks to increasing computational power, researchers have begun to investigate and understand the dynamic behavior of complex biological, cognitive, and social systems, using the concepts and tools of non-linear dynamical systems. In the next section, we will describe the key concepts of modern dynamical systems theory (complexity, self-organization, soft assembly, interaction dominance, and non-linearity). In the second section, we brie?y discuss some dynamical analysis techniques used in the cognitive sciences. In the third, we give some examples of the application of complex dynamical systems theory and analysis in cognitive science. In the last, we sketch some consequences of the widespread applicability of dynamical approaches to understanding neural, cognitive, and social systems.