Some ceramics bond to living bone through a bone-like apatite layer which is formed on their surfaces in the living body. The formation of the apatite layer is induced by Si-OH or Ti-OH groups on their surfaces. These findings provide us with a biomimetic process with which to form a bone-like apatite layer on metals and organic polymers. Titanium metal and its alloys form a thin alkali titanate layer on their surfaces when they are subjected to alkaline solution and heat treatments. Thus, treated metals form a dense, uniform bone-like apatite layer on their surfaces in acellular simulated body fluid (SBF) with ion concentrations nearly equal to those of human blood plasma. Organic polymers form apatite nuclei on their surfaces when they are placed on CaO-SiO2-based glass grains soaked in SBF. Thus, treated polymers form a dense, uniform bone-like apatite layer on their surfaces in SBF or other solutions highly supersaturated with respect to the apatite. The thickness of the apatite layer increases with increasing soaking time in the solution. The composition and structure of the apatite can be controlled by ion concentrations in the solution. The adhesive strengths of the apatite layer to the metal substrates are very high, and those to the polymer substrates can be considerably increased by glow discharge pretreatment of the substrates.