The paper surveys the microfoundations, empirical evidence, and estimation issues of the aggregate matching function. Several microeconomic matching mechanisms have been proposed, but none is universally accepted. An aggregate matching function, where hires depend on vacancies and unemployment, has been successfully estimated for many countries. The Cobb-Douglas form with constant returns to scale performs well. Recent studies use disaggregated data to refine aggregate estimates and suggest future research directions. The matching function models frictions in labor markets, such as information asymmetry, worker heterogeneity, and coordination failures. It captures the effects of these frictions on equilibrium outcomes using a small number of variables. The function is used to study wage and price determination and has been influential in equilibrium models of wage and employment. The paper discusses the key idea behind the matching function, evidence supporting it, and its theoretical foundations. It covers microfoundations, including mismatch, coordination failures, worker heterogeneity, ranking, stock-flow matching, and aggregation over distinct markets. Empirical methods and findings are also discussed, including Beveridge curves, aggregate studies, sectoral studies, and micro studies. The matching function is estimated using data on unemployment and vacancies, with the Beveridge curve showing the relationship between these variables. Estimated Beveridge curves slope downward but shift over time. Direct estimates of the matching function provide insights into its properties, with most studies finding a Cobb-Douglas form with constant returns to scale. The paper also discusses the role of worker heterogeneity, including search intensity and reservation wages, and the impact of mismatch and imbalance on the matching function. It highlights the importance of considering these factors in empirical studies. The matching function is also discussed in the context of stock-flow matching, where the interaction between stocks and flows of workers and vacancies is considered. The paper concludes that the aggregate matching function is a useful tool for understanding labor market frictions and their effects on unemployment and job creation. It emphasizes the importance of considering microfoundations and empirical evidence in the analysis of the matching function.The paper surveys the microfoundations, empirical evidence, and estimation issues of the aggregate matching function. Several microeconomic matching mechanisms have been proposed, but none is universally accepted. An aggregate matching function, where hires depend on vacancies and unemployment, has been successfully estimated for many countries. The Cobb-Douglas form with constant returns to scale performs well. Recent studies use disaggregated data to refine aggregate estimates and suggest future research directions. The matching function models frictions in labor markets, such as information asymmetry, worker heterogeneity, and coordination failures. It captures the effects of these frictions on equilibrium outcomes using a small number of variables. The function is used to study wage and price determination and has been influential in equilibrium models of wage and employment. The paper discusses the key idea behind the matching function, evidence supporting it, and its theoretical foundations. It covers microfoundations, including mismatch, coordination failures, worker heterogeneity, ranking, stock-flow matching, and aggregation over distinct markets. Empirical methods and findings are also discussed, including Beveridge curves, aggregate studies, sectoral studies, and micro studies. The matching function is estimated using data on unemployment and vacancies, with the Beveridge curve showing the relationship between these variables. Estimated Beveridge curves slope downward but shift over time. Direct estimates of the matching function provide insights into its properties, with most studies finding a Cobb-Douglas form with constant returns to scale. The paper also discusses the role of worker heterogeneity, including search intensity and reservation wages, and the impact of mismatch and imbalance on the matching function. It highlights the importance of considering these factors in empirical studies. The matching function is also discussed in the context of stock-flow matching, where the interaction between stocks and flows of workers and vacancies is considered. The paper concludes that the aggregate matching function is a useful tool for understanding labor market frictions and their effects on unemployment and job creation. It emphasizes the importance of considering microfoundations and empirical evidence in the analysis of the matching function.