We use a panel of historical patent data covering a large range of countries over the past century to study the evolution of innovation across time and space and its effect on productivity. We document a substantial rise of international knowledge spillovers as measured by patent citations since the 1990s. This rise is mostly accounted for by an increase in citations to US and Japanese patents in fields of knowledge related to computation, information processing, and medicine. We estimate the causal effect of innovation induced by international spillovers on sectoral output per worker and total factor productivity (TFP) growth in a panel of country-sectors from 2000 to 2014, as well as on aggregate income per capita since 1960. To assess causality, we develop a shift-share instrument that leverages pre-existing citation linkages across countries and fields of knowledge, as well as heterogeneous countries' exposure to technology waves. On average, an increase of one standard deviation in log-patenting activity increases sectoral output per worker growth by 1.1 percentage points. We find results of similar magnitude for sectoral TFP growth and long-run aggregate income per capita growth.