What is needed for poor countries to catch up with rich ones? This paper first documents the role of human capital, physical capital, and financial development in convergence in manufacturing labor productivity across countries, and then examines the influence of economic structure and financial development at the aggregate level. Using industry-level data from manufacturing industries in a large set of countries over the period 1980-2022, we show that manufacturing industries exhibit strong unconditional convergence over time, but there is variation in the pace of convergence: Greater reliance on human capital in an industry is linked to faster convergence, whereas dependence on physical capital has no bearing. Instead, industries with a greater dependence on physical capital see convergence only if there is sufficient financial development. At the country level, we find that convergence tends to be faster as countries shift away from agriculture (which typically requires less human capital), and towards industrial production or services. Furthermore, poorer countries that initially have a higher share of agriculture in their GDP have been shifting away from agriculture at a faster rate, which may have contributed to the observed aggregate convergence. Greater financial development is also linked to faster convergence at the country level.