Gas-liquid membrane contactors that were based on hollow fiber membranes are the example of highly effective hybrid separation processes in the field of membrane technology. Membranes provide a fixed and well-determined interface for gas/liquid mass transfer without dispensing one phase into another while their structure (hollow fiber) offers very large surface area per apparatus volume resulted in the compactness and modularity of separation equipment. In many cases, stated benefits are complemented with high separation selectivity typical for absorption technology. Since hollow fiber membrane contactors are agreed to be one of the most perspective methods for CO2 capture technologies, the major reviews are devoted to research activities within this field. This review is focused on the research works carried out so far on the applications of membrane contactors for other gas-liquid separation tasks, such as water deoxygenation/ozonation, air humidity control, ethylene/ethane separation, etc. A wide range of materials, membranes, and liquid solvents for membrane contactor processes are considered. Special attention is given to current studies on the capture of acid gases (H2S, SO2) from different mixtures. The examples of pilot-scale and semi-industrial implementation of membrane contactors are given.