Additive manufacturing has made it possible to create complicated geometries and lattice structures, and it is also the greatest approach for producing nature-inspired cellular structures. Triply periodic minimal surface (TPMS) cellular structure, which is additively built, has a high strength-to-weight ratio, making it useful in various applications, including structural weight reduction, biomedical, aerospace, and impact absorption. TPMS is a natural-inspired surface with zero mean curvature and a local minimal area. The type of structure, loading mechanism, unit cell characteristics, and relative density significantly affect the structure’s strength and stiffness. As a result, this article will cover the history, classification, characteristics, manufacturing processes, failure mechanism, and applications of the TPMS.