In this article, we show that historical naturalistic theories of biological function can meet central desiderata, while ahistorical alternatives cannot. To this end, we develop a comprehensive taxonomy of naturalistic theories of function and malfunctioning and argue that all possible ahistorical theories are unable to meet the distinction challenge (i.e. explaining why different traits have different functions) and the futile functioning challenge (i.e. allowing functions and malfunctions even when the fulfilment of the function serves no further purpose). In contrast, the selected effects theory and other historical theories can easily meet these two challenges. We, therefore, have good reason to leave ahistorical theories behind.