Worldwide, more than 85% of all chemical products are manufactured with the help of catalysts. Virtually all transition metals of the periodic table are active as catalysts or catalyst promoters. Catalysts are divided into homogeneous catalysts, which are soluble in the reaction medium, and heterogeneous catalysts, which remain in the solid state. A heterogeneous metal catalyst typically consists of the active metal component, promoters, and a support material. In some cases, the metallic state itself forms the active ingredient. However, this situation is largely restricted to precious metal catalysts and to some base metals used under reducing conditions. In most cases and especially in homogeneous catalysis, it is a metal compound or a complex that forms the active catalyst. Catalysis can be rather puzzling as a given metal can catalyze a variety of different chemical transformations, while the same substrate, passed over different catalysts, can give different products. It is therefore helpful to be familiar with the fundamentals of catalytic science before being exposed to the uncountable applications, which form the backbone of industrial chemistry. Examples of practical importance are used in this paper to highlight important principles of catalysis. (Contains 8 figures and 5 schemes.)