The absorption cooling/heating system is an old technology that has been relegated by the more efficient mechanical vapour compression systems. However, if they were driven by residual heat or solar thermal energy, advanced absorption technologies for cooling or heating could supply current demand and have a much lesser impact on the environment. With the cost of electricity rising and the climate change more and more in evidence, it would be a positive move towards energy saving. Since the absorber is recognized the key component of the absorption system due to the complex heat and mass transfer process that take place there, the improvement of the absorption process would mean reducing the absorber and desorber sizes to make them more compact, or reducing the system driving temperature for low grade temperature applications. The objective of this paper is to identify, summarize, and review the experimental studies dealing with the enhancement of vapour absorption processes in absorbers by means of passive techniques i.e. advanced surface designs and the use of additives and nanofluids. This review also includes an exhaustive and detailed scrutiny on absorption processes in falling film, spray and bubble mode absorbers for different working fluids, evidencing the experimenting techniques, operating conditions, and latest advances in terms of heat and mass transfer enhancement in absorbers. Finally, the paper contains suggestions for future work to be carried out to obtain mass transfer enhancement in absorbers and absorption cooling/heating systems.