This paper studies the dynamics of fertility in 180 countries in the period 1950-2015 and investigates the determinants of the onset of fertility transitions. The application of Phillips and Sul's (2007) test to fertility rates provides evidence of convergence in three groups of countries. This information is used to distinguish the transitioning countries from those not transitioning. The estimation of the year of onset of the fertility transition is 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. The instruments for per-capita income are the trade-weighted world income (Acemoglu et al., 2008) and the oil price shock (Brueckner and Schwandt, 2015). Mortality is instrumented with the predicted mortality (Acemoglu and Johnson, 2007), and mothers' education with the years of schooling of people aged 40-64. These results are confirmed by the application of Lewbel's (2012) methods where identification is based on heteroskedasticity.