The theoretical investigation of the structure of metabolic systems has recently attracted increasing interest. In this chapter, the basic concepts of metabolic pathway analysis are described and various applications are outlined. In particular, the concepts of nullspace and elementary flux modes are explained. The presentation is illustrated by a simple example from tyrosine metabolism and a system describing lysine production in Corynebacterium glutamicum. The latter system gives rise to 37 elementary modes, 36 of which produce lysine with different molar yields. The examples illustrate that metabolic pathway analysis is a useful tool for better understanding the complex architecture of intracellular metabolism, for determining the pathways on which the molar conversion yield of a substrate-product pair under study is maximal, and for assigning functions to orphan genes (functional genomics). Moreover, problems emerging in the modeling of large networks are discussed. An outlook on current trends in the field concludes the chapter.