The convergence debate has significantly influenced the growth theory debate, highlighting the relationship between convergence and the validity of alternative growth theories. This paper surveys the convergence literature, discussing different definitions of convergence and the methodologies used to investigate them. It shows that despite some impressions to the contrary, there is considerable agreement among the results. The research on convergence has established new stylized facts regarding cross-country growth regularities, such as 'persistence' and 'bi-modality'. It has also brought to light the existence of large technological and institutional differences across countries and has led to new methodologies for quantifying and analyzing these differences. This provides a new information base for analyzing technological and institutional diffusion and for further development of growth theory. The paper discusses the link between the growth theory controversy and the issue of convergence, cataloging different definitions and methodological approaches used for convergence research. It provides a brief description of different concepts of convergence, including convergence within vs. across economies, convergence in terms of growth rate vs. income level, β-convergence vs. σ-convergence, unconditional vs. conditional convergence, club convergence, TFP-convergence, and deterministic vs. stochastic convergence. The paper reviews initial evidence on convergence based on informal specifications of cross-section regressions and presents the formal, model-based growth-convergence equation that has become the mainstay of convergence research. It also reviews cross-section results based on formal specifications, including discussions of 'club convergence'. The panel approach to convergence study is reviewed, including research on TFP-convergence. The time series approach to convergence analysis is also reviewed. The distribution approach to convergence is discussed, including research on σ-convergence. The paper concludes that convergence research has had impressive achievements and has opened up useful new lines of research.The convergence debate has significantly influenced the growth theory debate, highlighting the relationship between convergence and the validity of alternative growth theories. This paper surveys the convergence literature, discussing different definitions of convergence and the methodologies used to investigate them. It shows that despite some impressions to the contrary, there is considerable agreement among the results. The research on convergence has established new stylized facts regarding cross-country growth regularities, such as 'persistence' and 'bi-modality'. It has also brought to light the existence of large technological and institutional differences across countries and has led to new methodologies for quantifying and analyzing these differences. This provides a new information base for analyzing technological and institutional diffusion and for further development of growth theory. The paper discusses the link between the growth theory controversy and the issue of convergence, cataloging different definitions and methodological approaches used for convergence research. It provides a brief description of different concepts of convergence, including convergence within vs. across economies, convergence in terms of growth rate vs. income level, β-convergence vs. σ-convergence, unconditional vs. conditional convergence, club convergence, TFP-convergence, and deterministic vs. stochastic convergence. The paper reviews initial evidence on convergence based on informal specifications of cross-section regressions and presents the formal, model-based growth-convergence equation that has become the mainstay of convergence research. It also reviews cross-section results based on formal specifications, including discussions of 'club convergence'. The panel approach to convergence study is reviewed, including research on TFP-convergence. The time series approach to convergence analysis is also reviewed. The distribution approach to convergence is discussed, including research on σ-convergence. The paper concludes that convergence research has had impressive achievements and has opened up useful new lines of research.