This paper provides a comprehensive review and forward-looking perspective on matching methods for causal inference. Matching methods aim to replicate the conditions of a randomized experiment by creating comparable treated and control groups in observational studies, thereby reducing bias due to covariates. The paper highlights the growing popularity of matching methods in various fields such as economics, epidemiology, medicine, and political science, but notes that the literature is scattered across disciplines. It defines matching broadly as any method that equates the distribution of covariates between treated and control groups, including 1:1 matching, weighting, and subclassification. The paper outlines the key steps in implementing matching methods: defining a distance measure, performing the matching, assessing the quality of the matched samples, and estimating the treatment effect. It discusses various distance measures, including exact matching, Mahalanobis distance, propensity scores, and linear propensity scores. The paper also covers different matching methods such as nearest neighbor matching, optimal matching, ratio matching, and methods like subclassification, full matching, and weighting adjustments. A significant focus is placed on diagnosing the quality of the matched samples, emphasizing the importance of assessing covariate balance. The paper suggests that well-specified regression models can be effective for estimating treatment effects when matching results in highly imbalanced samples. Finally, it provides guidance on future research directions and practical considerations for researchers interested in using matching methods.This paper provides a comprehensive review and forward-looking perspective on matching methods for causal inference. Matching methods aim to replicate the conditions of a randomized experiment by creating comparable treated and control groups in observational studies, thereby reducing bias due to covariates. The paper highlights the growing popularity of matching methods in various fields such as economics, epidemiology, medicine, and political science, but notes that the literature is scattered across disciplines. It defines matching broadly as any method that equates the distribution of covariates between treated and control groups, including 1:1 matching, weighting, and subclassification. The paper outlines the key steps in implementing matching methods: defining a distance measure, performing the matching, assessing the quality of the matched samples, and estimating the treatment effect. It discusses various distance measures, including exact matching, Mahalanobis distance, propensity scores, and linear propensity scores. The paper also covers different matching methods such as nearest neighbor matching, optimal matching, ratio matching, and methods like subclassification, full matching, and weighting adjustments. A significant focus is placed on diagnosing the quality of the matched samples, emphasizing the importance of assessing covariate balance. The paper suggests that well-specified regression models can be effective for estimating treatment effects when matching results in highly imbalanced samples. Finally, it provides guidance on future research directions and practical considerations for researchers interested in using matching methods.