Since the early 1990s, there has been a renaissance in the study of regional growth, spurred by new models, methods and data. We survey a range of modelling traditions, and some formal approaches to the 'hard problem' of regional economics, namely the joint consideration of agglomeration and growth. We also review empirical methods and findings based on natural experiments, spatial discontinuity designs, and structural models. Throughout, we give considerable attention to regional growth in developing countries. Finally, we highlight the potential importance of processes that are specific to regional decline, and which deserve greater research attention.