Among many artificial bone repair materials, tantalum has excellent biocompatibility, corrosion resistance, and osseointegration ability, which is suitable as a replacement material for bone defects in load-bearing parts of the human body. Porous tantalum prepared by additive manufacturing (AM) technology can achieve precise and individualized control of surface composition, porous structure, and mechanical properties, which can greatly meet clinical needs and become one of the hot spots in the field of bone repair materials. However, surface inertness, limited osseointegration, and lack of bioactivity are still the main problems of AM porous tantalum. The research progress on the functionalization of AM porous tantalum bone repair materials in China and abroad were introduced from the perspectives of surface modification methods and topological structure optimization. Several typical surface modification methods were summarized, and their advantages and disadvantages were analyzed. Suitable topological characteristics not only optimized the matching mechanical properties between the implant and host bone, but also facilitated the establishment of effective bone integration between AM porous tantalum. The research progress of AM porous tantalum topology optimization in recent years was reviewed. The effects of porosity, pore size, and pore geometry on the mechanical and biological functions of AM porous tantalum were summarized.