Cognitive stability and flexibility are regarded as key ingredients of goal-directed behavior. This review introduces dynamical systems as a theoretical framework for studying cognitive flexibility and stability. Following a gentle introduction to dynamical systems theory, we discuss how cognitive flexibility and stability can be operationalized and examined through the lens of such models. Drawing from recent advances in dynamical systems theory, we argue that various models of cognitive flexibility and stability, ranging from models of spiking neurons to models of human task switching to models of collective animal behavior, can be understood in terms of the same mathematical principles of low-dimensional dynamical systems. These principles suggest a trade-off between cognitive flexibility and stability inherent to dynamical system models of varying complexity. We conclude by discussing the consequences of this unified view and examine its explanatory scope in terms of behavioral and neural correlates of cognitive flexibility and stability.