This paper provides a comprehensive review of the Analytic Hierarchy Process (AHP) since its inception, focusing on methodological developments rather than applications. The authors discuss key areas such as problem modeling, pairwise comparisons, judgment scales, derivation methods, consistency indices, incomplete matrices, weight synthesis, sensitivity analysis, and group decision-making. AHP, a multi-criteria decision-making (MCDM) method, has been widely used in various fields, including banking, manufacturing, and strategic selection. The method involves hierarchical structuring of criteria, pairwise comparisons using ratio scales, priority derivation through methods like the geometric mean or eigenvalue, consistency checks, handling incomplete matrices, and aggregation of local priorities. The paper also addresses the rank reversal phenomenon, sensitivity analysis, and group decision-making techniques. Despite theoretical debates, AHP remains a popular tool due to its ease of use and intuitive structure, supported by user-friendly software like Expert Choice. Future developments may focus on improving hierarchy construction, addressing rank reversal, and integrating other decision-making methods.This paper provides a comprehensive review of the Analytic Hierarchy Process (AHP) since its inception, focusing on methodological developments rather than applications. The authors discuss key areas such as problem modeling, pairwise comparisons, judgment scales, derivation methods, consistency indices, incomplete matrices, weight synthesis, sensitivity analysis, and group decision-making. AHP, a multi-criteria decision-making (MCDM) method, has been widely used in various fields, including banking, manufacturing, and strategic selection. The method involves hierarchical structuring of criteria, pairwise comparisons using ratio scales, priority derivation through methods like the geometric mean or eigenvalue, consistency checks, handling incomplete matrices, and aggregation of local priorities. The paper also addresses the rank reversal phenomenon, sensitivity analysis, and group decision-making techniques. Despite theoretical debates, AHP remains a popular tool due to its ease of use and intuitive structure, supported by user-friendly software like Expert Choice. Future developments may focus on improving hierarchy construction, addressing rank reversal, and integrating other decision-making methods.