Patent data have been exploited to track invention and international technology diffusion. We review evidence on research activity, international patenting, and income differences across countries. Guided by that evidence, we construct a model of ideas in the world economy that includes the decision of whether and where to patent them. The model makes precise connections between international patent statistics and cross-country differences in innovation, technology diffusion, market size, and strength of patent protection. We use it to organize our discussion of existing empirical studies, which typically focus on one of five core relationships: (i) national pools of knowledge and international spillovers from basic research; (ii) aggregate productivity and international technology diffusion from applied research; (iii) international patenting and the production of ideas, international diffusion, market sizes, and intellectual property regimes; (iv) the value of ideas and diffusion, market sizes, and the intellectual property regimes; or (v) investment in research and research productivity, the cost of research, and the value of ideas. While distinguishing between these five relationships proves useful, they are, of course, logically intertwined. Taking these interconnections into account will contribute to the goal of building a quantitative model of the creation, diffusion, and adoption of ideas in the global economy.