A new paradigm is emerging in modern drug discovery. It is a fusion of traditional and modern medicine, phenotypic and targeted drug discovery, or systems and reductionist thinking. This is exemplified by using a combination of network medicine and high throughput screening. It blends the use of physiologically relevant biological systems with the high throughput and statistical robustness of modern assay technologies. The basic principles of network theory and tools of network medicine are described. Scale-free networks and their organizing principles are discussed. They are emergent properties of living, autopoietic systems. This includes networks of people who do high throughput screening (HTS), and microscopic networks of ions, metabolites, DNA, RNA, proteins, lipids, carbohydrates, viruses, bacteria, fungi, human cells and tissues. Databases have been constructed based on the metabolome, genome, transcriptome, proteome, lipidome, glycocode, virome, bacteriome and many others. Modern HTS can be used to examine the interactions of many parts of the complex human network. High content screening (HCS) can look at perturbations that occur when test compounds are added to single cells. Allo-network drugs can have effects far beyond a single protein and can be transmitted to other cells. Interactions and hidden connections can be revealed, with the goal of developing new drugs that have few, if any harmful side effects and are effective against multi-drug resistant cancer cells or bacteria.