Titanium alloys based on orthorhombic titanium aluminide Ti2AlNb are promising refractory materials for aircraft engine parts in the operating temperature range from 600–700 °C. Parts made of Ti2AlNb-based alloys by traditional technologies, such as casting and metal forming, have not yet found wide application due to the sensitivity of processability and mechanical properties in chemical composition and microstructure compared with commercial solid-solution-based titanium alloys. In the last three decades, metal additive manufacturing (MAM) has attracted the attention of scientists and engineers for the production of intermetallic alloys based on Ti2AlNb. This review summarizes the recent achievements in the production of O-phase-based Ti alloys using MAM, including the analysis of the feedstock materials, technological processes, machines, microstructure, phase composition and mechanical properties. Powder bed fusion (PBF) and direct energy deposition (DED) are the most widely employed MAM processes to produce O-phase alloys. MAM provides fully dense, fine-grained material with a superior combination of mechanical properties at room temperature. Further research on MAM for the production of critical parts made of Ti2AlNb-based alloys can be focused on a detailed study of the influence of post-processing and chemical composition on the formation of the structure and mechanical properties, including cyclic loading, fracture toughness, and creep resistance.