The absorber in which heat and mass transfer phenomena occur simultaneously is one of the most critical components in the absorption system. It has the most significant influence on the performance and the size of the absorption system. During the absorption process, heat and mass transfer resistances exist in both liquid and vapor regions, so that the heat transfer mode should be carefully selected to reduce them. The objective of this paper is to review the previous papers analysing mathematical models of simultaneous heat and mass transfer phenomena during the absorption process. The most conventional working fluids ($H_2O$LiBr and $NH_3/H_2O$) are considered and the most common absorption modes (falling film and bubble mode) are dealt with in this review.