Additive Manufacturing (AM) or rapid prototyping technologies are presented as one of the best options to produce customized prostheses and implants with high-level requirements in terms of complex geometries, mechanical properties, and short production times. The AM method that has been more investigated to obtain metallic implants for medical and biomedical use is Electron Beam Melting (EBM), which is based on the powder bed fusion technique. One of the most common metals employed to manufacture medical implants is titanium. Although discovered in 1790, titanium and its alloys only started to be used as engineering materials for biomedical prostheses after the 1950s. In the biomedical field, these materials have been mainly employed to facilitate bone adhesion and fixation, as well as for joint replacement surgeries, thanks to their good chemical, mechanical, and biocompatibility properties. Therefore, this study aims to collect relevant and up-to-date information from an exhaustive literature review on EBM and its applications in the medical and biomedical fields. This AM method has become increasingly popular in the manufacturing sector due to its great versatility and geometry control.