We highlight some important conceptual issues that biologists should take into account when teaching evolutionary biology or communicating it to the public. We first present conclusions from conceptual development research on how particular human intuitions, namely design teleology and psychological essentialism, influence the understanding of evolution. We argue that these two intuitions form important conceptual obstacles to understanding evolution that should be explicitly addressed during instruction and public communication. Given that a major issue in evolution is understanding how very different forms may share common ancestry — antievolutionists have argued that this is inconceivable — we suggest that evolutionary developmental biology (evo-devo), which provides concepts and evidence that large morphological change is possible, could be used to address the intuitions that organisms have fixed essences (psychological essentialism) and that their structure indicates some kind of intentional design (design teleology).