A (quite) large set of experiments has been undertaken to assess the potential for evolutionary changes in invertebrates under current and future climate change conditions. These experimental studies have established some key principles that could affect climate change adaptation, yet there remain substantial obstacles in reaching a meaningful predictive framework. This Review starts with exploring some of the traits considered in individuals and approaches used in assessing evolutionary adaptation relevant to climate, and some of the core findings and their substantial limitations, with a focus on Drosophila. We interpret results in terms of adaptive limits based on population processes versus fundamental mechanistic limits of organisms. We then consider the challenges in moving towards a predictive framework and implications of the findings obtained to date, while also emphasizing the current limited context and the need to broaden it if links to changes in natural populations are to be realized.