Knowledge flows within and across countries may have important consequences for both productivity and innovation. We use data on 1.5 million patents and 4.5 million citations to estimate knowledge flows at the frontier of technology across 147 subnational regions during 1975–1996 within the frame of a gravity-like equation. We estimate that only 20% of average knowledge is learned outside the average region of origin, and only 9% is learned outside the country of origin. However, knowledge in the computer sector flows substantially farther, as does knowledge generated by technological leaders. In comparison with trade flows, we see that knowledge flows reach much farther. External accessible R&D gained through these flows has a strong positive effect on innovative activity for a panel of 113 European and North American regions over 22 years.