There are a few patterns in nature that are striking even to casual observers. These include patterns of species richness associated with latitude, elevation, rainfall and area. Current thinking suggests that a number of primary mechanisms determine richness variation and that these differ depending on the type of pattern and the biome to which they apply. Prominent among the many hypotheses that attempt to explain the latitudinal diversity gradient (LDG) are those based either on climate or on historical factors such as past biome area. Climate-based and historically-based hypotheses have been regarded as competing alternatives, but there is growing acknowledgement that both are important. The evolutionary speed hypothesis (ESH) is one of several climate-based hypotheses. According to this hypothesis the LDG is generated by thermally mediated asymmetries in evolutionary speed and diversification. Here we identify five relationships predicted by the ESH and survey the literature for empirical evidence for and against these relationships. We find these five relationships are supported by a number of empirical studies. However, there are gaps in this evidence that require further work and, because the relationship between temperature and species richness is negative when water is limited, a modification to the ESH is necessary. Additionally, we suggest that diversity patterns associated with area, temperature and water availability might all be influenced by a common mechanism associated with biologically available energy and its influence on the tempo of evolution. Rates of genetic evolution might also be influenced by spatial heterogeneity and rates of biotic and abiotic environmental change, potentially introducing positive feedbacks between diversification and genetic evolution.