Models of membrane reactors (MRs) and catalytic membranes are presented by taking into account the advantages of the separation provided by the membranes. In particular, a 1D mathematical model is presented for tubular reactors considering a cylindrical symmetry, which is modeled by first- or second-order differential equations depending on the importance played by the axial diffusion. The permeation through the membrane is described by a specific transport model. Progresses in estimating the effect of external mass transfer in the gaseous films and inhibition phenomena limiting the permeation through the membranes are described, also introducing the so-called polarization and inhibition maps allowing the immediate evaluation of the influence of these phenomena on MR performance. Moreover, process intensification metrics are presented as additional nonconventional parameters useful for the identification of the operating condition ranges making a process more profitable.