Understanding the evolution of reaction norms remains a major challenge in ecology and evolution. Investigating evolutionary divergence in reaction norm shapes between populations and closely related species is one approach to providing insights. Here we use a meta-analytic approach to compare divergence in reaction norms of closely related species or populations of animals and plants across types of traits and environments. We quantified mean-standardized differences in overall trait means (Offset) and reaction norm shape (including both Slope and Curvature). These analyses revealed that differences in shape (Slope and Curvature together) were generally greater than differences in Offset. Additionally, differences in Curvature were generally greater than differences in Slope. The type of taxon contrast (species vs. population), trait, organism, and the type and novelty of environments all contributed to the best-fitting models, especially for Offset, Curvature, and the total differences (Total) between reaction norms. Congeneric species had greater differences in reaction norms than populations, and novel environmental conditions increased the differences in reaction norms between populations or species. These results show that evolutionary divergence of curvature is common and should be considered an important aspect of plasticity, together with slope. Biological details about traits and environments, including cryptic variation expressed in novel environmental conditions, may be critical to understanding how reaction norms evolve in novel and rapidly changing environments.