Over the last decade, we have witnessed an increased recognition of the importance of 3D culture models to study various aspects of cell physiology and pathology, as well as to engineer implantable tissues. As compared to well-established 2D cell-culture systems, cell/tissue culture within 3D porous biomaterials has introduced new scientific and technical challenges associated with complex transport phenomena, physical forces, and cell–microenvironment interactions. While bioreactor-based 3D model systems have begun to play a crucial role in addressing fundamental scientific questions, numerous hurdles currently impede the most efficient utilization of these systems. We describe how computational modeling and innovative sensor technologies, in conjunction with well-defined and controlled bioreactor-based 3D culture systems, will be key to gain further insight into cell behavior and the complexity of tissue development. These model systems will lay a solid foundation to further develop, optimize, and effectively streamline the essential bioprocesses to safely and reproducibly produce appropriately scaled tissue grafts for clinical studies.