Introducing a special journal issue by the same title, this article provides a foundation for seven other articles with a theoretical mission to better understand the forces and frictions through which migration comes about and is experienced. The collection seeks to contribute to migration theory by considering crosscutting themes related to the concepts of aspiration, desire and drivers of migration. This introductory article locates the three concepts within the development of migration scholarship. First, we show how a reappraisal of theory is grounded in influential developments in migration scholarship, such as the transnational turn, feminist approaches and, more recently, a growing theoretical interest in emotions and temporalities. Second, we examine the ways in which ‘aspiration’ and ‘desire’ have figured in migration theory. Sometimes treated as synonyms, the terms both belong to a broader semantic field of potentiality, yet connect with different theoretical approaches. Third, we address the rise of ‘drivers of migration’ as an analytical concept, noting how it seems to be replacing ‘causes’ and ‘determinants’ in the literature.