The fact that similar compounds may have very different properties has a large impact in several areas of chemistry. In drug discovery, almost every medicinal chemist working on lead optimization has faced unexpected large ‘jumps’ in activity due to small changes in structure, that is, activity cliffs. A number of computational approaches have been developed to detect and quantify activity cliffs and help to understand, and eventually predict, structure–activity relationships (SAR) in compound data sets. Although activity cliffs do exist, the identification and quantification of cliffs have to proceed with caution because one may identify ‘false positive cliffs’. In addition to apparent cliffs due to inaccurate determinations of activity, computationally identified cliffs can be artifacts attributed to the molecular representation and quantitative definition of ‘high’ structural similarity. This paper brings together and discusses, in a brief and integrated manner, some of the major aspects that raise the question whether all the activity cliffs detected in compound data sets are facts or artifacts.