The paper presents the review of the literature on income-level convergence(catching-up). The analysis includes convergence defined as the tendency toward equalization of income levels between countries. Unlike typical survey papers, the article focuses on the identification of weaknesses in the hitherto empirical studies on convergence. Apart from the standard types of the catching-up process (beta and sigma convergence), papers with the alternative measures of convergence(gamma and rho) are also analyzed. Both these elements constitute the value added of this research. The authors conclude that despite many empirical approaches, there is still much room for proposing new theoretical and empirical methods to analyze the catching-up process. Among others, studies that use hidden Markov models in the analysis of convergence are absent.