A number of drug withdrawals in recent years have been related to cardiovascular toxicity associated with undesirable blockade of the hERG potassium channel. A promiscuous target, hERG has been demonstrated to interact with pharmaceuticals of widely varying structure. Computational and statistical modeling efforts encompassing homology modeling, pharmacophore and quantitative structure-activity relationship models, and also various classification methods, are aimed at defining the molecular features that confer hERG inhibitory activity and understanding the structure-activity relationships that govern hERG-drug interactions. The organization-wide adoption of hERG models is driven by their ability to produce specific and testable structural hypotheses that lead to compounds devoid of hERG liability.