Driving is a multitasking activity that requires drivers to manage their attention among various driving- and non-driving-related tasks. When one models drivers as continuous controllers, the discrete nature of drivers' control actions is lost and with it an important component for characterizing behavioral variability. A proposal is made for the use of cognitive architectures for developing models of driver behavior that integrate cognitive and perceptual-motor processes in a serial model of task and attention management. A cognitive architecture is a computational framework that incorporates built-in, well-tested parameters and constraints on cognitive and perceptual-motor processes. All driver models implemented in a cognitive architecture necessarily inherit these parameters and constraints, resulting in more predictive and psychologically plausible models than those that do not characterize driving as a multitasking activity. These benefits are demonstrated with a driver model developed in the ACT-R cognitive architecture. The model is validated by comparing its behavior to that of human drivers navigating a four-lane highway with traffic in a fixed-based driving simulator. Results show that the model successfully predicts aspects of both lower-level control, such as steering and eye movements during lane changes, and higher-level cognitive tasks, such as task management and decision making. Many of these predictions are not explicitly built into the model but come from the cognitive architecture as a result of the model's implementation in the ACT-R architecture.