While poverty reduction remains central in the Post-2015 Agenda, its determinants remain debated in the literature, especially the role of structural conditions related to governance. This paper provides an assessment of two key dimensions: the global adoption of MDGs and state capacity. We do so by studying whether they facilitated convergence in income poverty measures, using cross-section and panel methods, with data on 89 developing economies for the period 1990-2013. We find that poverty headcount and gap measures tended to decrease faster in countries with initially higher income poverty. Such convergence accelerated after 2000, suggesting that MDGs adoption was instrumental to poverty reduction. However, this still leaves unexplained substantial variation in poverty reduction performance across countries. Such variation is explained by state capacity: countries with greater ability to administer their territories in 1990 experienced faster income poverty reduction and were more likely to have achieved the MDG target. This result is insensitive to robust regression methods and to a large set of controls (initial level of income, dependence on natural resources, education and health inputs, dependence on foreign aid, ethnic fractionalization, regional effects, and a set of governance variables). As good governance and effective institutions are included in the Sustainable Development Goals, this result provides empirical justification for this move, suggesting that more effective states could be crucial to sustain the development progress achieved so far.