Nickel–titanium (NiTi) is a shape-memory alloy, a type of material whose name is derived from its ability to recover its original shape upon heating to a certain temperature. NiTi falls under the umbrella of metallic materials, offering high superelasticity, acceptable corrosion resistance, a relatively low elastic modulus, and desirable biocompatibility. There are several challenges regarding the processing and machinability of NiTi, originating from its high ductility and reactivity. Additive manufacturing (AM), commonly known as 3D printing, is a promising candidate for solving problems in the fabrication of near-net-shape NiTi biomaterials with controlled porosity. Powder-bed fusion and directed energy deposition are AM approaches employed to produce synthetic NiTi implants. A short summary of the principles and the pros and cons of these approaches is provided. The influence of the operating parameters, which can change the microstructural features, including the porosity content and orientation of the crystals, on the mechanical properties is addressed. Surface-modification techniques are recommended for suppressing the Ni ion leaching from the surface of AM-fabricated NiTi, which is a technical challenge faced by the long-term in vivo application of NiTi.