This paper aims to systematically explore the relationship between affect, cognition, and driving behaviours. Whereas some driving models partially address drivers' affective factors, the majority of them have focused on cognitive aspects. Thus, it would be helpful to construct an affect-integrated driving behaviour research model. First, I briefly assessed the current driving models and identified critical cognitive elements commonly found among those models. Next, the mechanisms of affective effects on those cognitive processes were described. Then, I showed the effects of affective states on driving performance. Finally, a conceptual model for affect-related driving behaviour research was proposed and followed by discussions from the theoretical and practical perspectives. This review helps researchers construct a more naturalistic and generic driving behaviour model, conceptualise affect detection research with a clearer idea of what affect needs to be detected and why, and develop an affect regulation model and adaptive system for multiple drivers.