Dual tasks are a common phenomenon in everyday life. In dual-task contexts, we perform two component tasks in temporal overlap, which usually results in impaired performance in one or both of these component tasks relative to single-task contexts. Numerous studies have examined dual-task interference at the level of response selection, but only few studies addressed the cognitive representation of a dual task and the cognitive mechanisms controlling these representations. The present review outlines recent empirical findings and theoretical developments concerning these two issues. In detail, the review focuses on different components of a cognitive dual-task representation, including the representation of component-task specific information (i.e., information about the goal and stimulus-response mapping of a component task), the representation of component-task order information (i.e., information about the order in which the component tasks have to executed), and the representation of dual-task identity information (i.e., information about which two component tasks have to be performed). A particular emphasis is placed on the cognitive representation of dual-task identity information, which is examined in a recent research line employing the task-pair switching logic as an empirical approach. By conceptualizing a dual-task representation as a hierarchical multi-component representation, the review integrates the research line on the cognitive representation of dual-task identity information with those on the representation of component-task specific information and of component-task order information. Based on this conceptualization, the review provides a new theoretical contribution to dual-task research and highlights an integrative perspective on the different components of cognitive dual-task representations.