Endogenous growth has set a new paradigm for macroeconomic analysis. This paper overviews the most relevant theoretical contributions of this literature for the analysis of open economies, highlighting their implications both for the effects of cross-country integration on output convergence and for the overall growth performance of the integrated economy, as compared to that of an identical group of autarchic countries. The literature is divided into three major classes, studying, respectively, the effects of factor mobility, the role of international trade, and the consequences of technology diffusion.The main conclusion is that interactions with other countries play a key role in determining a nation's long-run rate of growth. From a theoretical viewpoint, some of the results of closed economy models of growth are in fact overturned by assuming that capital is mobile across borders, that countries can trade with each other, or that technologies diffuse internationally. However, the models presented in this survey often move the problem of explaining the differences in countries' growth performances one step backwards. Differences in structural parameters (such as those describing preferences and technologies), disparities in policy variables (such as the rate of taxation), asymmetries in the degree of international mobility of factors of production, dissimilarities in the patterns of technology diffusion, all these should be explained by a theory of growth in open economies, not simply assumed. Some contributions in this direction have already come, but much more need to be done. Indeed, the only way of explaining differences in output per capita between integrated countries is assuming that at least one factor is immobile between physical capital, human capital, or technology. Moreover, convergence dynamics can only be achieved by assuming some degree of stickiness in factor accumulation or transferability. Once it is recognized that these characteristics are necessary for an endogenous growth model to be able to explain differences in the countries' growth performances, the key point is to choose which factor is the most likely to be immobile. Apparently, the theoretical literature produced so far has reached a broad consensus that the most promising channels in order to explain the differences in growth performances across countries is knowledge diffusion, both in human capital accumulation and in research. The way in which the spillovers are modelled, however, still lacks the necessary microfoundations: the conclusions reached so far are often based on weaker bases than one would like to have. More careful analyses of the factors determining the shape and the patterns of international spillovers, capable of matching the findings of the growing empirical research, and of giving a guide to future applied analyses, are still required.