Electron beam melting (EBM) process is an additive manufacturing process largely used to produce complex metallic components made of high-performance materials for aerospace and medical applications. Especially, lattice structures made by Ti-6Al-4V have represented a hot topic for the industrial sectors because of having a great potential to combine lower weights and higher performances that can also be tailored by subsequent heat treatments. However, the little knowledge about the mechanical behaviour of the lattice structures is limiting their applications. The present work aims to provide a comprehensive review of the studies on the mechanical behaviour of the lattice structures made of Ti-6Al-4V. The main steps to produce an EBM part were considered as guidelines to review the literature on the lattice performance: (1) design, (2) process and (3) post-heat treatment. Thereafter, the correlation between the geometrical features of the lattice structure and their mechanical behaviour is discussed. In addition, the correlation among the mechanical performance of the lattice structures and the process precision, surface roughness and working temperature are also reviewed. An investigation on the studies about the properties of heat-treated lattice structure is also conducted.