Mediums claim to be able to communicate with the deceased. Such claims attract a considerable amount of public interest and, if valid, have important implications for many areas of psychology. For over 100 years, researchers have tested alleged mediums. This work has obtained mixed results and provoked a considerable amount of methodological debate. This paper reviews the key issues in this debate, describes how the authors devised a method of testing that aimed to prevent the many problems that have hindered past research, and how they then used this method to test several professional mediums. The results of this work did not support the existence of genuine mediumistic ability. Competing interpretations of these results are discussed, along with ways in which the methodology presented in the paper could be used to assess conceptually similar, but non-paranormal, claims made in clinical, occupational and forensic contexts.