This work reviews the development of computational fluid dynamics (CFD) modeling for hydrogen separation, with a focus on high temperature membranes to address industrial requirements in terms of membrane systems as contactors, or in membrane reactor arrangements. CFD modeling of membranes attracts interesting challenges as the membrane provides a discontinuity of flow, and therefore cannot be solved by the Navier-Stokes equations. To address this problem, the concept of source has been introduced to understand gas flows on both sides or domains (feed and permeate) of the membrane. This is an important solution, as the gas flow and concentrations in the permeate domain are intrinsically affected by the gas flow and concentrations in the feed domain and vice-versa. In turn, the source term will depend on the membrane used, as different membrane materials comply with different transport mechanisms, in addition to varying gas selectivity and fluxes. This work also addresses concentration polarization, a common effect in membrane systems, though its significance is dependent upon the performance of the membrane coupled with the operating conditions. Finally, CFD modeling is shifting from simplified single gas simulation to industrial gas mixtures, when the mathematical treatment becomes more complex.