Nb, Ta, and Zr are the favorable nontoxic and allergy-free alloying elements suitable for use in titanium alloys for biomedical applications. Low-rigidity titanium alloys composed of nontoxic and allergy-free elements are receiving considerable attention. The advantage of low-rigidity titanium alloys in the healing of bone fracture and bone remodeling is successfully proven by using tibia of rabbit as a fracture model. Ni-free superelastic and shape memory titanium alloys for biomedical applications are being actively developed. The mechanical properties such as fatigue and fretting fatigue are important from the viewpoint of mechanical properties, which may be collectively referred to as mechanical biocompatibilities in the broad sense, in addition to the rigidity, i.e. Young’s modulus. Bioactive surface modifications of titanium alloys for biomedical applications are very important for achieving further biocompatibility.