Student achievement varies widely across developed countries, but the source of these differences is not well understood. One obvious candidate, and a major focus of research and policy discussions both in the United States and abroad, is teacher quality. Research and common sense tell that good teachers can have a tremendous impact on their students' learning. But what, exactly, makes some teachers more effective than others? Can systematic evidence be provided that teachers' cognitive skills matter for student achievement? Do smarter teachers make for smarter students? And if so, how might education systems recruit teachers with stronger cognitive skills in the U.S.? To investigate these questions, the authors look at whether differences in the cognitive skills of teachers can help explain differences in student performance across developed countries. The authors consider data from the Organization for Economic Cooperation and Development (OECD), an association of 36 largely developed countries that has assessed nationally representative samples of both adults and students in reading and math. The authors use these data to estimate the effects of teacher cognitive skills on student achievement across 31 OECD countries. They find that teachers' cognitive skills differ widely among nations--and that these differences matter greatly for students' success in school. An increase of one standard deviation in teacher cognitive skills is associated with an increase of 10 to 15 percent of a standard deviation in student performance. This implies that as much as one quarter of the gaps in average student performance across the countries in the study would be closed if each of them were to raise their teachers' cognitive skills to the level of those in the highest-ranked country, Finland. The authors also investigate two explanations for why teachers in some countries are smarter than in others: differences in job opportunities for women and in teachers' salaries compared to those of other professions. They find that teachers have lower cognitive skills, on average, in countries with greater non-teaching job opportunities for women in high-skill occupations and where teaching pays relatively less than other professions. These findings have clear implications for policy debates here in the U.S., where teachers earn some 20 percent less than comparable college graduates.