The unique combination of superelasticity, shape-memory property, high corrosion resistance, and relative softness makes nickel-titanium (NiTi) shape-memory alloys an ideal choice for biomedical fixing elements, porous scaffolds, and load-sharing devices personalized for the specific patient. Additive manufacturing technology allows incorporating architected porosities into design, as well as anatomically tailored designs, but introduces process-dependent challenges concerning such factors as nickel volatilization, oxygen absorption, residual stress, surface roughness, pore imperfections, appearance of secondary phases, and nickel ions release. The key problem discussed in this article is what kind of relation should be established between processes of laser powder-bed fusion (LPBF), electron beam powder-bed fusion (EPBF), and directed energy deposition (DED) and various implant types according to geometry, transformation stability, mechanical compatibility, surface conditions, and biological safety criteria. Evidence concerning the use of NiTi in additive manufacturing process is presented below depending on the type of parts: dense transformation-sensitive elements, porous load-sharing structures, and patient-specific fixation devices. LPBF technology is recommended for precise geometry patient-specific implants and for stiffness-controlled fixation systems owing to the ability to provide dense material and create lattice structures, although it requires a highly controlled scanning pattern, atmosphere, hatch distance, and finishing process. DED technology can be justified in the case of porous bulk NiTi parts when lowering stiffness and achieving effective load sharing is critical, with reported porosity ranging from 12 to 36%, reversible strains from 2 to 4%, elastic modulus of about 18 GPa, and smaller tribocorrosion tracks than those of DED Ti-6Al-4V specimens. EPBF technology allows using vacuum conditions and lower contamination risk, but has biomedical applications restricted owing to inconsistent reports on phases composition and superelastic behavior. All the technologies require careful surface treatment due to the importance of this feature for corrosion resistance, osseointegration, nickel ions release and bacterial attachment: polishing, oxidation, electropolishing, nanotubes growth, HA-coating application, and polymer brush coating have been studied for this purpose.