This paper provides a comprehensive survey of the convergence literature, exploring different definitions of convergence and the methodologies used to study it. It highlights the link between convergence and the growth theory debate, particularly the distinction between neoclassical growth theory (NCGT) and new growth theories (NGT). The paper reviews four main approaches to convergence research: cross-section, panel, time-series, and distribution methods. Despite some criticisms, the research has led to significant advancements, including the establishment of new stylized facts about cross-country growth regularities and the development of methodologies for quantifying technological and institutional differences. The paper also discusses the evolution of convergence concepts, such as unconditional and conditional convergence, and the role of human capital. It concludes that while the convergence debate has not fully resolved the growth theory controversy, it has contributed to the adaptation and evolution of both NCGT and NGT, providing valuable insights into economic growth.This paper provides a comprehensive survey of the convergence literature, exploring different definitions of convergence and the methodologies used to study it. It highlights the link between convergence and the growth theory debate, particularly the distinction between neoclassical growth theory (NCGT) and new growth theories (NGT). The paper reviews four main approaches to convergence research: cross-section, panel, time-series, and distribution methods. Despite some criticisms, the research has led to significant advancements, including the establishment of new stylized facts about cross-country growth regularities and the development of methodologies for quantifying technological and institutional differences. The paper also discusses the evolution of convergence concepts, such as unconditional and conditional convergence, and the role of human capital. It concludes that while the convergence debate has not fully resolved the growth theory controversy, it has contributed to the adaptation and evolution of both NCGT and NGT, providing valuable insights into economic growth.