The new strategy of tissue engineering, and regenerative medicine at large, is to construct biomimetic matrices to mimic nature's hierarchical structural assemblages and mechanisms of simplicity and elegance that are conserved throughout genera and species. There is a direct spatial and temporal relationship of morphologic and molecular events that emphasize the biomimetism of the remodeling cycles of the osteonic corticocancellous bone versus the "geometric induction of bone formation," that is, the induction of bone by "smart" concavities assembled in biomimetic matrices of macroporous calcium phosphate-based constructs. The basic multicellular unit of the corticocancellous bone excavates a trench across the bone surface, leaving in its wake a hemiosteon rather than an osteon, that is, a trench with cross-sectional geometric cues of concavities after cyclic episodes of osteoclastogenesis, eventually leading to osteogenesis. The concavities per se are geometric regulators of growth-inducing angiogenesis and osteogenesis as in the remodeling processes of the corticocancellous bone. The concavities act as a powerful geometric attractant for myoblastic/myoendothelial and/or endothelial/pericytic stem cells, which differentiate into bone-forming cells. The lacunae, pits, and concavities cut by osteoclastogenesis within the biomimetic matrices are the driving morphogenetic cues that induce bone formation in a continuum of sequential phases of resorption/dissolution and formation. To induce the cascade of bone differentiation, the soluble osteogenic molecular signals of the transforming growth factor β supergene family must be reconstituted with an insoluble signal or substratum that triggers the bone differentiation cascade. By carving a series of repetitive concavities into solid and/or macroporous biomimetic matrices of highly crystalline hydroxyapatite or biphasic hydroxyapatite/β-tricalcium phosphate, we were able to embed smart biologic functions within intelligent scaffolds for tissue engineering of bone. The concavities assembled in the bioceramic constructs biomimetize the remodeling cycle of the corticocancellous bone and are endowed with multifunctional pleiotropic self-assembly capacities, initiating angiogenesis and bone formation by induction without the exogenous applications of the osteogenic-soluble molecular signals of the transforming growth factor β supergene family. The incorporation of specific biologic activities into biomimetic matrices by manipulating the geometry of the substratum, defined as geometric induction of bone formation, is now helping to engineer therapeutic osteogenesis in clinical contexts.