Detecting and determining the validity of local extinctions is an important conservation measure in order to uncover management failures. There are quantitative and qualitative methods that estimate extinction probability based on past sighting records. However, because current baselines about species' abundances and distributions in the sea were mostly established after humans had started affecting marine populations, researchers must often rely on historical data to elucidate past environmental conditions. We review early historical records from the Archipelago of Saint Paul's Rocks, together with data from recent expeditions, with the aim of testing the hypothesis that reef sharks (Carcharhinus spp.) have become extinct there. Our analyses are based on non-parametric probabilistic tests for extinction and on a qualitative framework to examine and judge as objectively as possible the likelihood of local extinction. Until the mid-20th century, visitors to St. Paul's Rocks invariably commented on the remarkable number of sharks around the Archipelago. These observations contrast with those of expeditions carried out during the last decade, which report no carcharhinid reef sharks while scuba diving in the archipelago, despite many more hours of underwater fieldwork than previous expeditions. All quantitative and qualitative methods conclude that the reef shark Carcharhinus galapagensis is locally extinct at St. Paul's Rocks after a sharp decrease in abundance that took place following the commencement of fishing. However, the persistence of occasional individuals of the once locally common Carcharhinus falciformis in the vicinity of the Archipelago, as a result of constant immigration of this oceanic species from outside the area, suggest that the population might recover if the present fishing pressure was removed.