How can total output and living standards continue to grow over time in the presence of essential non-renewable resources? We develop a theory of innovation in non-renewable resource extraction and economic growth. Firms increase their economically extractable reserves of non-renewable resources through investment in new extraction technology and reduce their reserves through extraction. Our model allows us to study the interaction between geology and technological change, and its effects on prices, total output growth, and the resource intensity of the economy. The model accommodates long-term trends in nonrenewable resource markets – namely stable prices and exponentially increasing extraction – for which we present data on 65 non-renewable resources extending back to 1700. The paper suggests that over the long term, increasing consumption of non-renewable resources fosters the development of new extraction technologies and hence offsets the exhaustion of higher quality resource deposits.