The knowledge of vapour-liquid equilibrium (VLE) and thermodynamic properties plays a pivotal role in the process development of absorption systems for acid gas capture in precombustion and postcombustion streams. A large number of thermodynamic modelling approaches for acid gas absorption in aqueous alkanolamine solutions are published in the literature. However, the reviews of these modelling techniques are limited and scattered. Moreover, poor guidelines exist for the selection of an appropriate modelling approach for the VLE prediction of the aforementioned system. Therefore, the current study presents a concise classification and review of classical thermodynamic models for acid gas absorption in aqueous alkanolamine solutions since their inception. The article systematically details the chronological development and highlights the major capabilities and limitations of classical thermodynamic approaches, namely, semiempirical models, activity coefficient models, and equation of state (and equation of state/excess Gibbs energy) models. A graphical comparison of VLE prediction by each classical approach is presented to form a general guideline in the selection of a suitable approach for process development studies. The review precisely discusses the issues, challenges, and future prospects of each classical thermodynamic approach in the context of application, complexity, and development.