In the inaugural lecture of the Oxford Martin Programme on the Impacts of Future Technology, Eric Drexler explores the implications of physical law for the future potential of nanotechnology, then describes the prospects for productive technologies that can solve global problems on the scale of climate change. A methodology grounded in physics and engineering can answer a limited yet illuminating range of questions about the potential of physical technology. This line of inquiry leads to a crucial question: What can physics tell us about the potential of advanced nanotechnologies? Well-established physical principles show that this potential embraces productive nanotechnologies that have the potential to transform the material basis of civilization. This prospect calls for re-evaluating both research opportunities and broader choices with consequences for the human future.