Many studies have recorded phenotypic changes in natural populations and attributed them to climate change. However, controversy and uncertainty has arisen around three levels of inference in such studies. First, it has proven difficult to conclusively distinguish whether phenotypic changes are genetically based or the result of phenotypic plasticity. Second, whether or not the change is adaptive is usually assumed rather than tested. Third, inferences that climate change is the specific causal agent have rarely involved the testing – and exclusion – of other potential drivers. We here review the various ways in which the above inferences have been attempted, and evaluate the strength of support that each approach can provide. This methodological assessment sets the stage for 11 accompanying review articles that attempt comprehensive syntheses of what is currently known – and not known – about responses to climate change in a variety of taxa and in theory. Summarizing and relying on the results of these reviews, we arrive at the conclusion that evidence for genetic adaptation to climate change has been found in some systems, but is still relatively scarce. Most importantly, it is clear that more studies are needed – and these must employ better inferential methods – before general conclusions can be drawn. Overall, we hope that the present paper and special issue provide inspiration for future research and guidelines on best practices for its execution.