This paper surveys the recent literature on the links between public debt and economic growth in advanced economies. We find that theoretical models yield ambiguous results. Whether high levels of public debt have a negative effect on long-run growth is thus an empirical question. While many papers have found a negative correlation between debt and growth, our reading of the empirical literature is that there is no paper that can make a strong case for a causal relationship going from debt to economic growth. We also find that the presence of thresholds and, more in general, of a non-monotone relationship between debt and growth is not robust to small changes in data coverage and empirical techniques. We conclude with a discussion of the challenges involved in measuring and defining public debt and some suggestions for future research which, in our view, should emphasize cross-country heterogeneity.