Target-Related Affinity Profiling (TRAP*) is a computational drug discovery technology that is based on ‘affinity fingerprints’, which are molecular descriptors derived from the protein binding preferences of small molecules. The underlying concepts of TRAP are reviewed. Affinity fingerprints are compared to molecular descriptors derived from chemical structures and shown to be a useful alternative for lead discovery. The TRAP screening process is described and two example applications are presented: I. the discovery of novel inhibitors of human intestinal carboxylesterase, and II. the discovery of novel inhibitors of cyclooxygenase-1 through the use of the affinity fingerprints of known cyclooxygenase-1 inhibitors. A summary of the complementary advantages of TRAP screening technology compared to traditional approaches to drug lead discovery concludes the review.