Pest species distribution modelling was designed to extrapolate risks in the biosecurity sector in order to protect agricultural crops against the spread of both endemic and introduced pest species. The need to identify sources of biological control agents for importation added to this demand. Independently, biogeographers mapped species distributions to interpolate their niche requirements. Recently the threat of climate change caused an explosion in demand for guidance on likely shifts in potential distributions of species. The different technology platforms in the two sectors resulted in divergence in their approaches to mapping actual and potential species distributions under rapidly changing environmental scenarios. Much of the contemporary discussion of species mapping ignores the lessons from the history of pest species distribution modelling. This has major implications for modelling of the non-equilibrium distributions of all species that occur with rapid climate change. The current review is intended to remind researchers of historical findings and their significance for current mapping of all species. I argue that the dream of automating species mapping for multiple species is an illusion. More modest goals and use of other approaches are necessary to protect biodiversity under current and future climates. Pest risk mapping tools have greater prospects of success because they are generic in nature and so able to be used both to interpolate and to extrapolate from field observations of any species based on climatic variables. In addition invasive species are less numerous and usually better understood, while the risk assessments are applied on regional scales in which climate is the dominant variable.