This review article focuses on instrumental variable (IV) estimators used in Mendelian randomization, a method for causal inference in observational studies. Mendelian randomization uses genetic variants as IVs to estimate the causal effect of an exposure on an outcome, assuming that these variants are randomly assigned at conception and thus not confounded by other factors. The article compares several IV estimation methods, including the ratio method, two-stage least squares (2SLS), likelihood-based methods, and semi-parametric methods. It discusses the assumptions, statistical properties, and practical considerations for each method, particularly in the context of weak instruments. The review also addresses the construction of confidence intervals and the handling of continuous and binary outcomes. The article provides practical guidelines for choosing the appropriate method based on the specific characteristics of the data and the research question. Key topics include the bias and coverage properties of estimators, the robustness to misspecification, and the efficiency of different methods. The review aims to complement existing literature by offering a comprehensive comparison and practical advice for researchers conducting Mendelian randomization studies.This review article focuses on instrumental variable (IV) estimators used in Mendelian randomization, a method for causal inference in observational studies. Mendelian randomization uses genetic variants as IVs to estimate the causal effect of an exposure on an outcome, assuming that these variants are randomly assigned at conception and thus not confounded by other factors. The article compares several IV estimation methods, including the ratio method, two-stage least squares (2SLS), likelihood-based methods, and semi-parametric methods. It discusses the assumptions, statistical properties, and practical considerations for each method, particularly in the context of weak instruments. The review also addresses the construction of confidence intervals and the handling of continuous and binary outcomes. The article provides practical guidelines for choosing the appropriate method based on the specific characteristics of the data and the research question. Key topics include the bias and coverage properties of estimators, the robustness to misspecification, and the efficiency of different methods. The review aims to complement existing literature by offering a comprehensive comparison and practical advice for researchers conducting Mendelian randomization studies.