This research presents a comprehensive bibliographic review from 2006 through 2020 about the state of the art of the compression−absorption cascade systems for refrigeration. In consequence of this review, this research identifies the significant development of systems that consider lithium bromide as a working fluid; however, the use of other working fluids has not been developed. This study is motivated toward the development of a parametric analysis of the cascade system using NH3-LiNO3, NH3-NaSCN and NH3-H2O in the absorption cycle and R134a in the compression cycle. In this study, the effect of the heat source temperature, condensation temperature in the compression cycle, the use of heat exchangers in the system (also known as economizers) and their contribution to the coefficient of performance is deepened numerically. The economizers evaluated are the following: an internal heat exchanger, a refrigerant heat exchanger, a solution refrigerant heat exchanger, and a solution heat exchanger. Mass and energy balance equations—appropriate equations to estimate the thermophysical properties of several refrigerant−absorbent pairs—were used to develop a thermodynamic model. The studied heat source temperature range was from 355 to 380 K, and the studied condensation temperature range in the compression cycle was from 281 to −291 K; additionally, the importance of each economizer on the coefficient of performance was numerically estimated. In this way, NH3-NaSCN solution in the absorption cycle and R134a in the compression cycle provided promising numerical results with the highest COPs (coefficient of performance).