A membrane reactor is a multifactional vessel used for H2 production. Hydrogen's three spectrum colors are dependent on carbon present. Two types of membrane with high permeability to hydrogen (polymeric and metallic) Hydrogen is produced in two systems: conventional reactors and membrane reactors (which separate and purify hydrogen in a single vessel). There are many types of membrane reactors according to design (catalytic membrane reactor (CMR), fixed bed reactor (FBMR), fluidized bed reactor (FBMR), etc. The transport mechanism of H2 through the membrane by a "sorption-diffusion mechanism" and the government equations that are used for membrane reactor modeling and simulation, such as continuity, momentum, mass, and heat transfer equations of the CMR, and the thickness of the membrane. These equations are solved by MATLAB, COMSOL, and the Finite Element Method to simulate the MR at different parameters: rate of conversion, rate of sweep gas, temperature, pressure, rate of H2 permeation through a membrane, and activity of the catalyst. We summarized theoretical studies for membrane reactors, including the operation conditions, type of hydrocarbon feed, type of production method, kind of catalyst, and heat effect.