In forensics, evidence such as DNA, fingerprints, bullets and cartridge cases, shoeprints or digital evidence is often compared, to infer if they come from the same or different sources. This helps to generate leads through database searches, where information from different investigations can be combined, if pieces of evidence are judged to have come from the same source. For specific pairs of comparisons, such as whether a particular cartridge case comes from a suspect's gun, an inference of a match can also be used as testimony in courts. We demonstrate how such matching problems fit into the record linkage framework commonly used in statistics and computer science, illustrating this using examples from DNA and firearms identification. We propose some ways that record linkage can inform forensic matching. Finally, we develop methodology to match accounts on anonymous marketplaces. In forensic matching, the stakes are high and the consequences of false arrests or wrongful convictions are severe. The field would benefit from a more principled way of developing matching methods.