The origin of species-rich insect–plant food webs has traditionally been explained by diversifying antagonistic coevolution between plant defences and herbivore counter-defences. However, recent studies combining paleoclimatic reconstructions with time-calibrated phylogenies suggest that variation in global climate determines the distribution, abundance and diversity of plant clades and, hence, indirectly influences the balance between speciation and extinction in associated herbivore groups. Extant insect communities tend to be richest on common plant species that have many close relatives. This could be explained either by climate-driven diffuse cospeciation between plants and insects, or by elevated speciation and reduced extinction in herbivore lineages associated with expanding host taxa (resources). Progress in paleovegetation reconstructions in combination with the rapidly increasing availability of fossil-calibrated phylogenies provide means to discern between these alternative hypotheses. In particular, the ‘Diffuse cospeciation’ scenario predicts closely matching main diversification periods in plants and in the insects that feed upon them, while the ‘Resource abundance-dependent diversification’ hypothesis predicts that both positive and negative responses of insect diversity are lagged in relation to host-plant availability. The dramatic Cenozoic changes in global climate provide multiple possibilities for studying the mechanisms by which climatic shifts may drive diversity dynamics in plants and insect herbivores.