Like zeolites that combine shape selectivity with catalysis, membranes combine separation with catalysis to enhance reaction rates. The dual functionality of zeolites derives from the nature of the catalytic material, whereas that of membranes derives from the nature of the reactor material. The catalyst in the membrane reactor can be a part of the membrane itself or be external to it (i.e., placed inside the membrane tube). The chief property of a membrane is its ability for selective permeation or permselectivity with respect to certain compounds. Organic membrane reactions are best carried out in reactors made of inorganic membranes, such as from palladium, alumina, or ceramics. Good descriptions of these reactions and the membranes used are available in many reviews, for example, Gryaznov (1986, 1992), Stoukides (1988), Armor (1989), Govind and Ilias (1989), Bhave (1991), Zaspalis and Burggraaf (1991), Hsieh (1989, 1991), Shu et al. (1991), Shieh (1991), Gellings and Bouwmeister (1992), Tsotsis et al. (1993b), Harold et al. (1994), Saracco and Specchia (1994), Sanchez and Tsotsis (1996). A recent trend has been to develop polymeric-inorganic composite type membranes formed by the deposition of a thin dense polymeric film on an inorganic support (Kita et al., 1987; Rezac and Koros, 1994, 1995; Zhu et al., 1996). Another class of membranes under development for organic synthesis is the liquid membrane (Marr and Kopp, 1982; Eyal and Bressler, 1993). The permselective barrier in this type of membrane is a liquid phase, often containing a dissolved “carrier” or “transporter” that selectively reacts with a specific permeate to enhance its transport rate through the membrane. Our main concern in this chapter will be with inorganic membrane reactors. We commence our treatment with an introduction to the exploitable features of membrane reactors (with no attempt to describe membrane synthesis). Then we describe the main variations in design and operating mode of these reactors, develop performance equations for the more important designs, and compare the performances of some important designs with those of the traditional mixed- and plug-flow reactors. Finally, we present a summary of the applications of membrane reactors in enhancing the rates of organic reactions.