Ontology matching is an integral part for establishing semantic interoperability. One of the main challenges within the ontology matching operation is semantic heterogeneity, i.e. modeling differences between the two ontologies that are to be integrated. The semantics within most ontologies or schemas are, however, typically incomplete because they are designed within a certain context which is not explicitly modeled. Therefore, external background knowledge plays a major role in the task of (semi-) automated ontology and schema matching. In this survey, we introduce the reader to the general ontology matching problem. We review the background knowledge sources as well as the approaches applied to make use of external knowledge. Our survey covers all ontology matching systems that have been presented within the years 2004–2021 at a well-known ontology matching competition together with systematically selected publications in the research field. We present a classification system for external background knowledge, concept linking strategies, as well as for background knowledge exploitation approaches. We provide extensive examples and classify all ontology matching systems under review in a resource/strategy matrix obtained by coalescing the two classification systems. Lastly, we outline interesting and yet underexplored research directions of applying external knowledge within the ontology matching process.