Several ecological and evolutionary hypotheses are based on the assumption that species reach their highest abundance in the centre of their range and decline in abundance toward the range edges. We reviewed empirical tests of this assumption, which we call the ‘abundant centre’ hypothesis. We found that of 145 separate tests conducted as part of 22 direct empirical studies, only 56 (39%) support the abundant centre hypothesis. More problematic than the percentage of studies that support the hypothesis is the finding that most studies inadequately sampled the species’ ranges. Only two of the studies analysed data that were collected throughout the species’ range. The remaining studies relied on data from a small number of points in their analysis, meaning that the range edges were severely under-sampled. Patterns of abundance across the entire range must be known to draw testable hypotheses about the consequences of species’ geographical abundance distributions. Indirect tests of the abundant centre hypothesis, in which ecological or evolutionary expectations of abundant centre distributions were examined, did not support or reject the abundant centre hypothesis overall. We conclude that more exploration of species’ abundance distributions is necessary and we suggest methods to use in future studies.