With the requirement of energy decarbonization, natural gas (NG) and hydrogen (H2) become increasingly important in the world’s energy landscape. The liquefaction of NG and H2 significantly increases energy density, facilitating large-scale storage and long-distance transport. However, conventional liquefaction processes mainly adopt electricity-driven compression refrigeration technology, which generally results in high energy consumption and carbon dioxide emissions. Absorption refrigeration technology (ART) presents a promising avenue for enhancing energy efficiency and reducing emissions in both NG and H2 liquefaction processes. Its ability to utilize industrial waste heat and renewable thermal energy sources over a large temperature range makes it particularly attractive for sustainable energy practices. This review comprehensively analyzes the progress of ART in terms of working pairs, cycle configurations, and heat and mass transfer in main components. To operate under different driven heat sources and refrigeration temperatures, working pairs exhibit a diversified development trend. The environment-friendly and high-efficiency working pairs, in which ionic liquids and deep eutectic solvents are new absorbents, exhibit promising development potential. Through the coupling of heat and mass transfer within the cycle or the addition of sub-components, cycle configurations with higher energy efficiency and a wider range of operational conditions are greatly focused. Additives, ultrasonic oscillations, and mechanical treatment of heat exchanger surfaces efficiently enhance heat and mass transfer in the absorbers and generators of ART. Notably, nanoparticle additives and ultrasonic oscillations demonstrate a synergistic enhancement effect, which could significantly improve the energy efficiency of ART. For the conventional NG and H2 liquefaction processes, the energy-saving and carbon emission reduction potential of ART is analyzed from the perspectives of specific power consumption (SPC) and carbon dioxide emissions (CEs). The results show that ART integrated into the liquefaction processes could reduce the SPC and CE by 10~38% and 10~36% for NG liquefaction processes, and 2~24% and 5~24% for H2 liquefaction processes. ART, which can achieve lower precooling temperatures and higher energy efficiency, shows more attractive perspectives in low carbon emissions of NG and H2 liquefaction.