The ascent of polypharmacology in drug development has many implications for disease therapy, most notably in the efforts of drug discovery, drug repositioning, precision medicine and combination therapy. The single- target approach to drug development has encountered difficulties in predicting drugs that are both clinically efficacious and avoid toxicity. By contrast, polypharmacology offers the possibility of a controlled distribution of effects on a biological system. This review addresses possibilities and bottlenecks in the efficient computational application of polypharmacology. The two major areas we address are the discovery and prediction of multiple protein targets using the tools of computer-aided drug design, and the use of these protein targets in predicting therapeutic potential in the context of biological networks. The successful application of polypharmacology to systems biology and pharmacology has the potential to markedly accelerate the pace of development of novel therapies for multiple diseases, and has implications for the intellectual property landscape, likely requiring targeted changes in patent law.