This paper studies the origins and consequences of international technology gaps. I develop an endogenous growth model where R&D efficiency varies across countries and productivity differences emerge from firm-level technology investments. The theory characterizes how innovation and learning determine technology gaps, trade and global income inequality. Countries with higher R&D efficiency are richer and have comparative advantage in more innovation-dependent industries where the advantage of backwardness is lower and knowledge spillovers are more localized. I estimate R&D efficiency by country and innovation-dependence by industry from R&D and bilateral trade data. Calibrating the model implies technology gaps, due to cross-country differences in R&D efficiency, account for around one-quarter to one-third of nominal wage variation within the OECD.