Back pain is one of the leading causes of disability worldwide and is frequently caused by degeneration of the intervertebral discs. The discs’ development, homeostasis, and degeneration are driven by a complex series of biochemical and physical extracellular matrix cues produced by and transmitted to native cells. Thus, understanding the roles of different cues is essential for designing effective cellular and regenerative therapies. Omics technologies have helped identify many new matrix cues; however, comparatively few matrix molecules have thus far been incorporated into tissue engineered models. These include collagen type I and type II, laminins, glycosaminoglycans, and their biomimetic analogues. Modern biofabrication techniques, such as 3D bioprinting, are also enabling the spatial patterning of matrix molecules and growth factors to direct regional effects. These techniques should now be applied to biochemically, physically, and structurally relevant disc models incorporating disc and stem cells to investigate the drivers of healthy cell phenotype and differentiation. Such research will inform the development of efficacious regenerative therapies and improved clinical outcomes.