Some fundamental aspects of the catalytic phenomenon are described in the introductory part of this chapter. Next, some different catalyst classifications are described based on catalytic action (acid–base, redox, metallorganic, and enzymatic) or catalytic environment (homogeneous and heterogeneous). Different aspects of homogeneous catalysis are examined in detail considering acid–base catalysis, catalysis promoted by metal transition complexes, and enzymatic catalysis. Heterogeneous catalysis is then examined describing gas–solid interactions in particular and adsorption isotherms useful for determining gas–solid interface area. Different heterogeneous catalysts are described, such as acid–base solid catalysts based on metal oxides and their mixtures, metal oxide catalysts acting as semiconductors, zeolites, and unsupported and supported metal catalysts. The most commonly employed supports are described together with techniques for their preparation and impregnation. Finally, catalyst-forming procedures are briefly described. Some exercises and associated MATLAB code are provided online.