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Aim: The aim was to understand the representativeness and accuracy of expert range maps and to explore alternative methods for mapping species distributions accurately. Location: Global. Time period: Contemporary. Major taxa studied: Terrestrial vertebrates and Odonata. Methods: We analysed the biases in 50,768 animal International Union for Conservation of Nature, Global Assessment of Reptile Distributions and BirdLife species maps and assessed the links between these maps and existing political boundaries and various non‐ecological boundaries to assess their accuracy for certain types of analyses. We cross‐referenced each species map with data from the Global Biodiversity Information Facility to assess whether maps captured the whole range of a species and what percentage of occurrence points fell within the assessed range of the species. In addition, we used a number of different methods to map diversity patterns and compared these with high‐resolution models of distribution patterns. Results: On average, 20–30% of the non‐coastal range boundaries of species overlapped with administrative national boundaries. In total, 60% of areas with the highest spatial turnover in species (high densities of species range boundaries marking high levels of shift in the community of species present) occurred at political boundaries, which was especially common in Southeast Asia. Different biases existed for different taxa, with gridded analysis in reptiles, river basins in Odonata (except the Americas) and county boundaries for amphibians in the USA. On average, up to half (25–46%) of the recorded range points of species fell outside their mapped distributions. Filtered minimum convex polygons performed better than expert range maps in reproducing modelled diversity patterns. Main conclusions: Expert range maps showed high bias at administrative borders in all taxa, but this was highest at the transition from tropical to subtropical regions. The methods used were inconsistent across space, time and taxa, and the ranges mapped did not match species distribution data. Alternative approaches can reconstruct patterns of distribution better than expert maps, and data‐driven approaches are needed to provide reliable alternatives to gain a better understanding of species distributions. [ABSTRACT FROM AUTHOR]