We review the characteristics of osteoblast differentiation and bone matrix synthesis. Bone in air breathing vertebrates is a specialized tissue that developmentally replaces simpler solid tissues, usually cartilage. Bone is a living organ bounded by a layer of osteoblasts that, because of transport and compartmentalization requirements, produce bone matrix exclusively as an organized tight epithelium. With matrix growth, osteoblasts are reorganized and incorporated into the matrix as living cells, osteocytes, which communicate with each other and surface epithelium by cell processes within canaliculi in the matrix. The osteoblasts secrete the organic matrix, which are dense collagen layers that alternate parallel and orthogonal to the axis of stress loading. Into this matrix is deposited extremely dense hydroxyapatite-based mineral driven by both active and passive transport and pH control. As the matrix matures, hydroxyapatite microcrystals are organized into a sophisticated composite in the collagen layer by nucleation in the protein lattice. Recent studies on differentiating osteoblast precursors revealed a sophisticated proton export network driving mineralization, a gene expression program organized with the compartmentalization of the osteoblast epithelium that produces the mature bone matrix composite, despite varying serum calcium and phosphate. Key issues not well defined include how new osteoblasts are incorporated in the epithelial layer, replacing those incorporated in the accumulating matrix. Development of bone in vitro is the subject of numerous projects using various matrices and mesenchymal stem cell-derived preparations in bioreactors. These preparations reflect the structure of bone to variable extents, and include cells at many different stages of differentiation. Major challenges are production of bone matrix approaching the in vivo density and support for trabecular bone formation. In vitro differentiation is limited by the organization and density of osteoblasts and by endogenous and exogenous inhibitors.