A membrane contactor is a device that achieves gas/liquid or liquid/liquid mass transfer without dispersion of one phase within another. This is accomplished by passing the fluids on opposite sides of a microporous membrane. By careful control of the pressure difference between the fluids, one of the fluids is immobilized in the pores of the membrane so that the fluid/fluid interface is located at the mouth of each pore. This approach offers a number of important advantages over conventional dispersed phase contactors, including absence of emulsions, no flooding at high flow rates, no unloading at low flow rates, no density difference between fluids required, and surprisingly high interfacial area. Indeed, membrane contactors typically offer 30 times more area than what is achievable in gas absorbers and 500 times what is obtainable in liquid/liquid extraction columns, leading to remarkably low HTU values. Although a number of membrane module geometries are possible, hollow fiber modules have received the most attention. In general, tube side mass transfer coefficients can be predicted with reasonable accuracy; on the other hand, shell side coefficients are more difficult to determine, and several research groups are currently addressing this problem. Membrane contactor technology has been demonstrated in a range of liquid/liquid and gas/liquid applications in fermentation, pharmaceuticals, wastewater treatment, chiral separations, semiconductor manufacturing, carbonation of beverages, metal ion extraction, protein extraction, VOC removal from waste gas, and osmotic distillation. This paper provides a general review of hollow fiber membrane contactors, including operating principles, relevant mathematics, and applications.