Quaternary climatic oscillations had a large impact on European biogeography. Alternation of cold and warm stages caused recurrent glaciations, massive vegetation shifts, and large-scale range alterations in many species. The Eurasian steppe biome and its grasslands are a noteworthy example; they underwent climate-driven, large-scale contractions during warm stages and expansions during cold stages. Here, we evaluate the impact of these range alterations on the late Quaternary demography of several phylogenetically distant plant and insect species, typical of the Eurasian steppes. We compare three explicit demographic hypotheses by applying an approach combining convolutional neural networks with approximate Bayesian computation. We identified congruent demographic responses of cold stage expansion and warm stage contraction across all species, but also species-specific effects. The demographic history of the Eurasian steppe biota reflects major paleoecological turning points in the late Quaternary and emphasizes the role of climate as a driving force underlying patterns of genetic variance on the biome level.