Hollow fiber membrane contactors have several advantages that make them a good alternative to conventional absorption processes in the gas industry, and they have attracted the interest of many researchers. However, critical issues such as wetting hinder applications of membranes on a wide scale. Wetting is the penetration of the liquid absorbent through membrane pores, reducing mass transfer and consequently affecting the CO2 absorption efficiency and lowering the effectiveness of the separation process. The availability of membranes that can maintain a high efficiency and remain stable over a long period of operation is the main factor that is required in order to implement membranes in the industry for absorption processes. The wetting phenomenon in hollow fiber membranes is the focus of this review, which offers a critical examination of the literature published on membrane wetting, highlighting the main factors that control the effectiveness of the membrane separation process. These factors include the liquid absorbent, the membrane morphology represented by pore size and porosity, and the mutual interaction between liquid absorbents and the membranes. All of these factors are discussed in detail in view of a better understanding of the wetting phenomenon. Furthermore, methods and approaches to prevent wetting in addition to perspectives for future research in the area are presented.