As global energy demand rose by 2.3% in comparison to the last year rate of 1.2%, fossil fuels, biofuels and natural gas are becoming increasingly important in power generation and production of the liquid fuels. However, the presence of the contaminants, such as H2S and CO2 in the derived products from these fuels is the cause of several operational and technical issues ranging from equipment corrosion, fouling, catalyst deactivation, and environmental pollution. Therefore, it is necessary to remove contaminants from these gaseous mixtures for their effective use for multiple applications. The objective of this review is to explore various experimental, theoretical and simulation approaches which are developed to improve the operation and design of different H2S and CO2 removal technologies. The fundamental thermodynamic and kinetic models for the acid gas removal processes through simulation, design related to their improvements in the absorber and the stripper through experimentation and simulation work and relevant optimization studies based on chemical absorption have been discussed. The simulation and experimental work focusing on physical absorption is also summarized. The experimental and simulation-based studies on blends of different solvents are presented. The comparison of various solvents related to H2S and CO2 removal techniques is demonstrated. Feasibility assessment of various H2S removal techniques via experimentation is presented. The effort for process intensification and new modifications has led to better understanding of acid gas removal techniques. Improvements are eminent in enhancing the efficiency of the absorber and stripper through reduction in the heat requirements. The scope of blends of various solvents for use at commercial scale and optimization of the operating conditions can lead to reduction in capital and operating cost. Finally, the future directions of research to improve the cleaning processes have been indicated.