“Catch-up” relates to the ability of a single country to narrow the gap in productivity and income vis-à-vis a leader country, while “convergence” refers to a trend towards a reduction of the overall differences in productivity and income in the world as a whole. Successful catch-up has historically been associated not merely with the adoption of existing techniques in established industries, but also with innovation, particularly of the organizational kind, and with inroads into nascent industries. This article discusses some of the perspectives that have emerged in the catching up literature. It extends the perspective to the most recent decades, compares cases of successful catch-up to less successful ones, and considers the lessons that may be drawn. Finally, it raises the question of what present day developing countries can learn, particularly with respect to policy, from the literature on innovation and catching up.