In the last decade, additive manufacturing (AM) processes have updated the fields of biomaterials science and drug delivery as they promise to realize bioengineered multifunctional devices and implantable tissue engineering (TE) scaffolds virtually designed by using computer-aided design (CAD) models. However, the current technological gap between virtual scaffold design and practical AM processes makes it still challenging to realize scaffolds capable of encoding all structural and cell regulatory functions of the native extracellular matrix (ECM) of health and diseased tissues. Indeed, engineering porous scaffolds capable of sequestering and presenting even a complex array of biochemical and biophysical signals in a time- and space-regulated manner, require advanced automated platforms suitable of processing simultaneously biomaterials, cells, and biomolecules at nanometric-size scale. The aim of this work was to review the recent scientific literature about AM fabrication of drug delivery scaffolds for TE. This review focused on bioactive molecule loading into three-dimensional (3D) porous scaffolds, and their release effects on cell fate and tissue growth. We reviewed CAD-based strategies, such as bioprinting, to achieve passive and stimuli-responsive drug delivery scaffolds for TE and cancer precision medicine. Finally, we describe the authors’ perspective regarding the next generation of CAD techniques and the advantages of AM, microfluidic, and soft lithography integration for enhancing 3D porous scaffold bioactivation toward functional bioengineered tissues and organs.