This review surveys the computational methods that have been developed with the aim of identifying drug candidates likely to fail later on the road to market. The specifications for such computational methods are outlined, including factors such as speed, interpretability, robustness and accuracy. Then, computational filters aimed at predicting "drug-likeness" in a general sense are discussed before methods for the prediction of more specific properties--intestinal absorption and blood-brain barrier penetration--are reviewed. Directions for future research are discussed and, in concluding, the impact of these methods on the drug discovery process, both now and in the future, is briefly considered.