Polypharmacology, which focuses on designing therapeutics to target multiple receptors, has emerged as a new paradigm in drug discovery. Polypharmacological effects are an attribute of most, if not all, drug molecules. The efficacy and toxicity of drugs, whether designed as single- or multitarget therapeutics, result from complex interactions between pharmacodynamic, pharmacokinetic, genetic, epigenetic, and environmental factors. Ultimately, to predict a drug response phenotype, it is necessary to understand the change in information flow through cellular networks resulting from dynamic drug-target interactions and the impact that this has on the complete biological system. Although such is a future objective, we review recent progress and challenges in computational techniques that enable the prediction and analysis of in vitro and in vivo drug-response phenotypes.