Interruptions of ongoing activities have spread since the development of and global increase in technology use and the general speeding in pace we all experience every day. Their negative effects are well known: decline in performance and emotional distress. However, the literature still needs to shed light on the exact cognitive mechanisms involved in the way users decide to reply to an interruption, on the effects of interruptions of different durations, and on factors influencing reactivation of task schemata and goals at resumption. Therefore, the aim of this article is to review the existing literature and models, uncover unresolved challenges, and propose new ways to confront them. We first review the substantive findings of recent decades from different domains (human-computer interaction, cognitive and experimental psychology, ergonomics), and their respective methodological and theoretical contributions. Then we propose a general and operationalized definition of an interruption; review the different cognitive models of attention, executive control, and working memory that best explain the impact of interruptions; describe current challenges and questions that remain open for future studies; and finally propose an integrative research framework, the DETOUR, which clarifies the cognitive processes at play during interruptions. We believe this work can directly affect the current state of the art, leading to new fundamental studies and applied solutions for the management of interruptions.