Artificial hydroxyapatite with chemical formula of Ca10(PO4)6(OH)2 is the best as bioceramics due to its composition and structure being similar with inorganic part of hard tissues. The alloys especially with Ti, Ni and Co contents are very promising as a kind of biomaterials due to their high strength and high toughness. The alloys as biomaterials need good final surface properties by proper surface treatment. By using clinical treatment with machining, cleaning, sterilization, we obtained Ti-oxides surface with 4-6 nm in thickness which are very good in property with chemical composition of TiO2 + Ti2O3 + TiO. However, the Ti-alloy with an artificial hydroxyapatite surface is even much better than that with the surface of Ti-oxides due to its high bioactivity. Human bones and human teeth with a chemical composition of Ca10(PO4)6(OH)2 and the structure of hydroxyapatite are commonly considered as bio-mineral. In nature the pears and shells are also a kind of bio-minerals. Our observations showed that human bone is a complex material with a layered composite structure. The hydroxyapatite mineral crystals that reinforce the organic proteinceous component are about 35 nm wide, irregular, plate-like crystals reside initially in the hole zones of the collagen microfibris: later fill available space within the collagen fibrils. At present paper nanostructure features of both bioceramics and biominerals have been characterized with comparison between each other's.