This paper studies the dynamics of fertility in 180 countries in theperiod 1950-2015 and investigates the determinants of the onset of fertility transitions. We find evidence of convergence in three groups of countries, and distinguish the transitioning countries from those not transitioning. The estimation of the year of onset of the fertility transitionis followed by an econometric analysis of the causes of this event. Instrumental-variable estimates show that increasing female education and reduced infant mortality are important determinants of fertility decline, while per-capita GDP has probably worked in the opposite direction. These results are confirmed by the application of Lewbel's (2012) methods where identification is based on heteroskedasticity.