The design of biomimetic porous scaffolds has been gaining attention in the biomedical sector lately. Shells, marine sponges, shark teeth, cancellous bone, sea urchin spine, and the armadillo armor structure are examples of biological systems that have already been studied to drive the design of innovative, porous, and multifunctional structures. Among these, triply periodic minimal surfaces (TPMSs) have attracted the attention of scientists for the fabrication of biomimetic porous scaffolds. The interest stems from their outstanding properties, which include mathematical controllable geometry features, highly interconnected porous architectures, high surface area to volume ratio, less stress concentration, tunable mechanical properties, and increased permeability. All these distinguishing features enable better cell adhesion, optimal integration to the surrounding tissue avoiding stress shieldings, a good permeability of fluid media and oxygen, and the possibility of vascularization. However, the sophisticated geometry of these TPMS-based structures has proven challenging to fabricate by conventional methods. The emergence of additive manufacturing (AM) and the enhanced manufacturing freedoms and flexibility it guarantees could solve some of the bottlenecks, thus leading to a surge of interest in designing and fabricating such structures in this field. Also, the feasibility of using AM technologies allows for obtaining size programmable TPMS printable in various materials, from polymers to metal alloys. Here, a comprehensive overview of 3D-printed TPMS porous structures is provided from a design for additive manufacturing (DfAM) and application perspective. First, design strategies, geometry design algorithms, and related topological optimization are introduced according to diverse requirements. Based on that, the performance control of TPMS and the pros and cons of the different AM processes for fabricating TPMS scaffolds are summarized. Lastly, practical applications of 3D-printed biomimetic TPMS porous structures for the biomedical field are presented to clarify the advantages and potential of such structures.