This paper develops a search-theoretic model of technological change that accounts for some puzzling trends in industrial research, patenting, and productivity growth. In the model, researchers sample from probability distributions of potential new production techniques. Past research generates a technological frontier representing the best techniques for producing each good in the economy. Technological breakthroughs, resulting in patents, become increasingly hard to find as the technological frontier advances. This explains why patenting has been roughly constant as research employment has risen sharply over the last forty years. Productivity is determined by the position of the technological frontier and hence by the stock of past research. If researchers sample from Pareto distributions, then productivity growth is proportional to the growth of the research stock. The Pareto specification accounts for why productivity growth has neither risen as research employment has grown nor fallen as patenting has failed to grow. The growth of research employment itself is driven, in equilibrium, by population growth. Calibrating the model's four parameters, the implied social return to research is over twenty percent.