This review covers the relatively short history of metabolic pathway analysis. Computer-aided algorithms for the synthesis of metabolic pathways are discussed. Important algebraic concepts used in pathway analysis, such as null space and convex cone, are explained. It is demonstrated how these concepts can be translated into meaningful metabolic concepts. For example, it is shown that the simplest vectors spanning the region of all admissible fluxes in stationary states, for which the term elementary flux modes was coined, correspond to fundamental pathways in the system. The concepts are illustrated with the help of a reaction scheme representing the glyoxylate cycle and adjacent reactions of aspartate and glutamate synthesis. The interrelations between pathway analysis and metabolic control theory are outlined. Promising applications for genome annotation and for biotechnological purposes are discussed. Armed with a better understanding of the architecture of cellular metabolism and the enormous amount of genomic data available today, biochemists and biotechnologists will be able to draw the entire metabolic map of a cell and redesign it by rational and directed metabolic engineering.