Advances in the field of genomics have enabled computational analysis of metabolic pathways at the genome scale. Singular attention has been devoted in the literature to stoichiometric approaches, and path-finding approaches, to metabolic pathways. Stoichiometric approaches make use of reaction stoichiometry when trying to determine metabolic pathways. Stoichiometric approaches involve elementary flux modes and extreme pathways. In contrast, path-finding approaches propose an alternative view based on graph theory in which reaction stoichiometry is not considered. Path-finding approaches use shortest path and k-shortest path concepts. In this article we give a critical overview of the theory, applications and key research challenges of stoichiometric and path-finding approaches to metabolic pathways.