Additive manufacturing (AM) technology has undergone an evolutionary process from fabricating test products and prototypes to fabricating end-user products—a major contributing factor to this is the continuing research and development in this area. AM offers the unique opportunity to fabricate complex structures with intricate geometry such as the lattice structures. These structures are made up of struts, unit cells, and nodes, and are being used not only in the aerospace industry, but also in the sports technology industry, owing to their superior mechanical properties and performance. This paper provides a comprehensive review of the mechanical properties and performance of both metallic and non-metallic lattice structures, focusing on compressive behaviour. In particular, optimisation techniques utilised to optimise their mechanical performance are examined, as well the primary factors influencing mechanical properties of lattices, and their failure mechanisms/modes. Important AM limitations regarding lattice structure fabrication are identified from this review, while the paucity of literature regarding material extruded metal-based lattice structures is discussed.