Inspired by natural porous architectures, numerous attempts have been made to generate porous structures. Owing to the smooth surfaces, highly interconnected porous architectures, and mathematical controllable geometry features, triply periodic minimal surface (TPMS) is emerging as an outstanding solution to constructing porous structures in recent years. However, many advantages of TPMS are not fully utilized in current research. Critical problems of the process from design, manufacturing to applications need further systematic and integrated discussions. In this work, a comprehensive overview of TPMS porous structures is provided. In order to generate the digital models of TPMS, the geometry design algorithms and performance control strategies are introduced according to diverse requirements. Based on that, precise additive manufacturing methods are summarized for fabricating physical TPMS products. Furthermore, actual multidisciplinary applications are presented to clarify the advantages and further potential of TPMS porous structures. Eventually, the existing problems and further research outlooks are discussed.