Catalytic reactors have widespread applications in producing chemicals. Developments in catalysis and reaction engineering in the 1930s-1940s enabled rational design of catalytic reactors. Mathematical modeling of reactors has improved understanding of factors like intra- and inter-particle diffusion. Fixed bed reactors are commonly used and can be adiabatic, nonadiabatic with external heat exchange, or operated with reverse gas flow. Modeling reactor performance requires considering transport phenomena and kinetics at macro and micro scales within the catalyst bed.