This paper sheds light on the global migration patterns of the past 40 years, and produces migration projections for the 21st century. To do this, we build a simple model of the world economy, and we parameterize it to match the economic and socio-demographic characteristics of the world in the year 2010. We conduct backcasting and nowcasting exercises, which demonstrate that our model fits very well the past and ongoing trends in international migration, and that historical trends were mostly governed by demographic changes. Then, we describe a set of migration projections for the 21st century. In line with the backcasts, our world migration prospects are mainly governed by socio-demographic changes. Using immigration restrictions or development policies to curb these pressures requires sealing borders or triggering unprecedented economic takeoffs in migrants’ countries of origin. Increasing migration is thus a likely phenomenon for the 21st century. Electronic supplementary material The online version of this article (10.1007/s10290-020-00402-1) contains supplementary material, which is available to authorized users.