The growth in detailed multi-omic profiling has created new opportunities to tailor clinical care and therapy to patient-level variations in disease phenotype. However, efforts towards precision medicine and personalized therapeutics are hampered by limitations in identifying biologically relevant signals that correlate with and underlie disease activity and therapeutic response from these growing arrays of data. These complexities are accentuated further when attempting to translate the new insights in disease pathobiology into new drug targets for treatment. Additionally, understanding how best to reposition existing drugs in the context of new data on disease pathogenesis remains a challenge. Network medicine provides one approach by which to comprehend these large data sets to identify better the key molecular and phenotypic signals that can function as disease and treatment biomarkers and that can be targeted for therapy. In this review, we discuss basic concepts in the application of network science to biological systems and then build on these concepts to discuss network-based approaches for identifying novel disease biomarkers, elucidating new drug targets, and repositioning existing drugs for new indications.