Constraint-based approaches have proved successful in analyzing complex metabolic networks. They restrict the range of all possible behaviors that a metabolic system can display under governing constraints. The set of all possible flux distributions over a metabolic network at steady state defines a polyhedral cone, the steady-state flux cone. This cone can be analyzed using an inner description, based on sets of generating vectors such as elementary modes or extreme pathways. We present a new constraint-based approach to metabolic network analysis, characterizing a metabolic network by its minimal metabolic behaviors and the reversible metabolic space. Our method uses an outer description of the flux cone, based on sets of non-negativity constraints. The resulting description is minimal and unique. We then study the relationship between inner and outer descriptions of the cone. We give a generic procedure to show how inner descriptions can be computed from the outer one. We use this procedure to explain why the size of the inner descriptions may be several orders of magnitude larger than that of the outer description. Our approach suggests a refined classification of reactions according to their reversibility type (irreversible, pseudo-irreversible, and fully reversible). Using these concepts, we improve an existing algorithm for identifying blocked and coupled reactions and devise a new algorithm for flux coupling analysis. We extend this analysis by introducing minimal direction cuts (MDCs) which prevent a target reaction from being performed in an undesired direction. We develop an algorithm which allows not only for computing MDCs in a metabolic network, but also for a direct calculation of minimal cut sets (MCSs). Based on our refined classification of reactions, we also provide a constraint-based approach for analyzing the changes in the overall capabilities of a metabolic network following a gene deletion. Flux coupling and gene deletion analysis help for identifying important reactions in metabolic networks. Alternatively, the essentiality of reactions can be assessed using control-effective flux (CEF) analysis, which is based on elementary modes. We compare CEF analysis with the use of a minimal generating set of the flux cone to elucidate crucial reactions.