Although it has been variously defined and discussed, the ‘species problem’ in evolutionary palaeontology actually consists of at least three separate but closely related questions: (1) What are species in living organisms? (the ‘species nature problem’); (2) To what degree can ‘species’ as recognized in living organisms be recognized in the fossil record? (the ‘species recognition problem’); (3) To the degree that species can be so recognized, to what degree can species be studied as modern species are, that is, what can we learn about the origin and evolution of species from fossils that we could not otherwise learn? This can be called the ‘species study problem’. A critical survey of the history of thinking about the nature and origin of species indicates that answers to at least two of these three questions (the first and third) have been remarkably persistent in both palaeontological and neontological views over the past 250 years, and the range of answers to them has changed remarkably little. The nature of Darwin's ideas on these issues, which has remained controversial, is an epitome of the persistent complexity and difficulty of the questions involved. This historical survey has a number of implications for modern palaeontological views of the nature and origin of species, including that the nature of species is a substantive (as opposed to a purely semantic) issue, likely to be decided empirically and not just theoretically, and that the roles of selection and isolation in the origin of species are likely diverse and complex.