Network Medicine applies network science approaches to investigate disease pathogenesis. Many different analytical methods have been used to infer relevant molecular networks, including protein-protein interaction networks, correlation-based networks, gene regulatory networks, and Bayesian networks. Network Medicine applies these integrated approaches to Omics Big Data (including genetics, epigenetics, transcriptomics, metabolomics, and proteomics) using computational biology tools and, thereby, has the potential to provide improvements in the diagnosis, prognosis, and treatment of complex diseases. We discuss briefly the types of molecular data that are used in molecular network analyses, survey the analytical methods for inferring molecular networks, and review efforts to validate and visualize molecular networks. Successful applications of molecular network analysis have been reported in pulmonary arterial hypertension, coronary heart disease, diabetes mellitus, chronic lung diseases, and drug development. Important knowledge gaps in Network Medicine include incompleteness of the molecular interactome, challenges in identifying key genes within genetic association regions, and limited applications to human diseases.