What makes people want to migrate to another country? This question spurs ever more data collection and research in migration studies, economics, sociology, psychology and other disciplines. We present the first systematic review of the resulting literature. The review covers 49 comparable studies that seek to determine how individual factors (such as educational attainment or employment status) and contextual factors (such as the quality of public services or the levels of violence and insecurity) help explain who wants to leave and who wants to stay. Across the diverse analyses, we examine 966 effects and define 32 determinants of migration aspirations. Some of these determinants have a consistent effect while others produce divergent or incocnclusive results. By means of innovative visual displays, we present the effects of each determinant in a way that accommodates attention to variations, exceptions and uncertainty. The factors that stand out as the most certain and steady drives of migration aspirations are young age and ties with current or former migrants. Other determinants -- especially dissatisfaction with public services, and exposure to violence and insecurity -- appear to raise migration aspirations even more consistently, but they have been addressed in fewer studies and therefore remain less certain.