Scaffold hopping refers to the computer-aided search for active compounds containing different core structures, which is a topic of high interest in medicinal chemistry. Herein foundations and caveats of scaffold hopping approaches are discussed and recent methodological developments analyzed. Despite the conceptual prevalence of pharmacophore methods for scaffold hopping, a variety of computational approaches have been successfully applied. In recent years, scaffold hopping calculations are increasingly carried out at the level of scaffolds rather than compounds, and scaffold queries increasingly abstract from chemical structures. In addition, relationships between compounds, scaffolds, and biological activities are beginning to be globally explored, beyond individual applications. Going forward, computational scaffold hopping is thought to benefit from the consideration of new scaffold concepts and the development of methods capable of guiding search calculations toward scaffolds that are likely to represent potent compounds.