Abstract: As a novel class of porous structures with smooth continuous surfaces and high specific surface area, triply periodic minimal surface (TPMS) structures have excellent properties such as high load-bearing capacity, high energy absorption rate, and good fatigue performance, which facilitate their application in a wide range of fields such as aerospace, biomedicine, acoustic isolation and absorption, etc. Due to its unique advantages in manufacturing complex topological structures, additive manufacturing (AM) technology has become a powerful tool for the manufacture of TPMS structures. However, various defects are introduced in AM and have essential impacts on the mechanical properties of the TPMS structures. A comprehensive and in-depth study on the mechanical properties of TPMS structures fabricated by AM is of great significance for evaluating and predicting the structural performance of TPMS structures and broadening their application in engineering. In this paper, the TPMS structures are firstly introduced in terms of structural forms, characteristics and application fields, and the recent important progresses are summarized, focusing on the key mechanical properties such as static compression, dynamic impact resistance and fatigue fracture. Secondly, the common techniques of AM for the fabrication of TPMS structures are discussed by taking the examples of selective laser melting (SLM) and selective laser sintering (SLS). Thirdly, the effects of defects introduced during AM on the mechanical properties of TPMS structures are reviewed, including residual stress, surface roughness and internal micropores. Finally, the challenges faced in practical applications of this field are summarized and future research directions are envisioned.