One contribution of 13 to a theme issue 'The major synthetic evolutionary transitions'. Using three examples drawn from animal systems, I advance the hypothesis that major transitions in multicellular evolution often involved the constitution of new cell-based materials with unprecedented morphogenetic capabilities. I term the materials and formative processes that arise when highly evolved cells are incorporated into mesoscale matter 'biogeneric', to reflect their commonality with, and distinctiveness from, the organizational properties of non-living materials. The first transition arose by the innovation of classical cell-adhesive cadherins with transmembrane linkage to the cytoskeleton and the appearance of the morphogen Wnt, transforming some ancestral unicellular holozoans into 'liquid tissues', and thereby originating the metazoans. The second transition involved the new capabilities, within a basal metazoan population, of producing a mechanically stable basal lamina, and of planar cell polarization. This gave rise to the eumetazoans, initially diploblastic (twolayered) forms, and then with the addition of extracellular matrices promoting epithelial-mesenchymal transformation, three-layered triploblasts. The last example is the fin-to-limb transition. Here, the components of a molecular network that promoted the development of species-idiosyncratic endoskeletal elements in gnathostome ancestors are proposed to have evolved to a dynamical regime in which they constituted a Turing-type reaction-diffusion system capable of organizing the stereotypical arrays of elements of lobe-finned fish and tetrapods. The contrasting implications of the biogeneric materialsbased and neo-Darwinian perspectives for understanding major evolutionary transitions are discussed.This article is part of the themed issue 'The major synthetic evolutionary transitions'.