Extinction of a species is difficult to detect, yet there are important conservation consequences of classifying an extant species as extinct or an extinct species as extant, and potentially significant costs of making the wrong classification. To deal with the uncertainties of detecting extinctions, some Critically Endangered species are tagged as ‘possibly extinct’ in the IUCN Red List. Recently developed methods allow calculating the probability that a species is already extinct, P(E), based on threats, time series of records of the species, the intensity of targeted surveys and other factors. We review the potential costs and benefits of classifying extinct and extant species as extinct, possibly extinct, and extant. Benefits of correct classification include the correct estimation of extinction rates, correct analysis of extinction correlates, appropriate allocation of resources, and (if extinct) the recognition of loss of the species. Costs of incorrectly classifying extant species as extinct include the “Romeo error” (premature cessation of conservation, leading to the possible extinction of the species), and the loss of scientific credibility upon rediscovery of presumed extinct species. Costs of incorrectly classifying extinct species as extant include inefficient use of resources and underestimating extinction rates. Based on these costs and benefits, we propose a framework for setting thresholds of P(E) for classifying species as extinct, possibly extinct, and extant.