Reduced graphs provide summary representations of chemical structures by collapsing groups of connected atoms into single nodes while preserving the topology of the original structures. This chapter reviews the extensive work that has been carried out on reduced graphs at The University of Sheffield and includes discussion of their application to the representation and search of Markush structures in patents, the varied approaches that have been implemented for similarity searching, their use in cluster representation, the different ways in which they have been applied to extract structure-activity relationships and their use in encoding bioisosteres.