Proteins do not exert their effects in isolation of one another, but interact together in complex networks. In recent years, sophisticated methods have been developed to leverage protein-protein interaction (PPI) network structure to improve several stages of the drug discovery process. Network-based methods have been applied to predict drug targets, drug side effects, and new therapeutic indications. In this paper we have two aims. First, we review the past contributions of network approaches and methods to drug discovery, and discuss their limitations and possible future directions. Second, we show how past work can be generalized to gain a more complete understanding of how drugs perturb networks. Previous network-based characterizations of drug effects focused on the small number of known drug targets, i.e., direct binding partners of drugs. However, drugs affect many more genes than their targets - they can profoundly affect the cell's transcriptome. For the first time, we use networks to characterize genes that are differentially regulated by drugs. We found that drug-regulated genes differed from drug targets in terms of functional annotations, cellular localizations, and topological properties. Drug targets mainly included receptors on the plasma membrane, down-regulated genes were largely in the nucleus and were enriched for DNA binding, and genes lacking drug relationships were enriched in the extracellular region. Network topology analysis indicated several significant graph properties, including high degree and betweenness for the drug targets and drug-regulated genes, though possibly due to network biases. Topological analysis also showed that proteins of down-regulated genes appear to be frequently involved in complexes. Analyzing network distances between regulated genes, we found that genes regulated by structurally similar drugs were significantly closer than genes regulated by dissimilar drugs. Finally, network centrality of a drug's differentially regulated genes correlated significantly with drug toxicity.