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High-strength, Low density periodic Ti-6Al-4V lattice materials built with additive manufacturing provide relatively widespread applications for aerospace, biomedicine, marine and other fields. In this paper, the reported compressive properties, failure modes, microstructure and the heat treatment of Selective laser melting (SLM) and Selective electron beam melting (SEBM) additive manufatured Ti-6Al-4V lattice materials are reviewed. According to statistics, the continuous and integrated lattice materials can be manufatured via SLM and SEBM. And more importantly, the compressive strength and yield strength of skeleton-based Diamond TPMS lattice materials can reach to 411.71 MPa and 317.48 MPa respectively, which are comparable to those of magnesium alloys. It is also be found that the main failure modes of Ti-6Al-4V lattice materials are 45° shearing fracture and horizontally fracture. Shearing fractured lattice materials have unique advantages in load-bearing capacity, while horizontally fractured lattice materials with smaller fluctuation in stress-strain curves, showing dominant superiority in energy absorption capacity. Heat treatment is an effective method to eliminate the residual stress, reduce the roughness and transform acicular α "martensite to α+β phase caused by additive manufacturing, and then increase the ductility of lattice materials without reducing or even increasing the strength of Ti-6Al-4V lattice materials. Finally, the existing disadvantages and future development trend of additive Ti-6Al-4V lattice materials are prospected.