Metabolism plays a central role in cell physiology and provides the cellular machinery for building biomolecules essential for growth. At the genome-scale, metabolism is made up of thousands of reactions interacting with one another. Untangling this complexity is key to understand how cells respond to genetic, environmental or therapeutic perturbations. Here we discuss the roles of two complementary strategies for the analysis of genome-scale metabolic models: constraint-based methods, such as flux balance analysis, and network science. Whereas constraint-based methods estimate metabolic flux on the basis of an optimization principle, networktheoretic approaches reveal emergent properties of the global metabolic connectivity. We highlight how the integration of both approaches promises to deliver insights on the structure and function of metabolic systems with wide-ranging implications in basic discovery science, precision medicine and industrial biotechnology.