Eponyms are a prominent feature of medical language. Many feel they have had their time and serve only to complicate medical education and conversation. Others argue that eponyms can make unmemorable concepts memorable, can concisely label complex concepts, and promote a valuable interest in medical history. It is frequently assumed that medical eponyms are marching towards extinction. However, this hypothesis has not been adequately tested. The fate of 8,636 eponyms from contemporary and historical registers is presented here. The annual usage of each eponym in PubMed indexed articles since 1900 is analysed with metrics of eponym prevalence, coinage and extinction. The fate of eponyms named for those implicated in Nazi war crimes is also measured. The analysis shows that more publications used an eponym in their title in 2014 than ever before. However, the proportion using an eponym title has fallen from a peak of 3% in 1991 to 2% today, while annual extinction of eponyms overtook coinage in the 1980s. This suggests that, while not in dramatic decline, they are perhaps losing market share to more scientific descriptions. There is no ambiguity in the fate of eponyms related to Nazi war crimes which have almost entirely fallen out of use in the last decade.