Two biogenic materials from mussels are attracting attention from scientists: calcium carbonate ($CaCO_3$), the most widely studied biomineral that composes the shell - or nacre - of mussels; dopamine, a small catechol-containing biomimetic molecule of adhesive foot proteins secreted by mussels. We have incorporated these two materials into the biomimetic mineralization process to produce stable vaterite microspheres, which are the most unstable crystalline phase of $CaCO_3$. Spherical vaterite crystals were readily formed within two minutes in the presence of dopamine undergoing polymerization, and were preserved for over two months in aqueous solution. The prolonged maintenance of spherical structure is attributed to the affinitive interaction between calcium in the vaterite microspheres and catechols from dopamine retarding the dissolution of vaterite and the growth of calcite crystals. The mussel-inspired inducement of a stable vaterite phase suggests a facile route for the synthesis of complex organic-inorganic hybrid materials utilizing biogenic systems. Thus-formed vaterite microspheres were readily transformed to carbonated hydroxyapatite crystals when incubated in a simulated body fluid at human body temperature. We found that dopamine not only stabilized the vaterite phase but also influenced the level of conversion to carbonated hydroxyapatites. Considering that carbonated hydroxyapatites are highly bioresorbable, similar to natural bone and dentin, the synthesis of a mussel-inspired hybrid material showing good in vitro bone bioactivity should present a new prospect for future applications in the treatment of bone defects and bone degenerative diseases. We could also synthesize hollow $CaCO_3$ microspheres and their composite with biodegradable polymer fibers having enhanced in vitro bone bioactivity by utilizing gaseous $CO_2$ in the presence of dopamine. $CO_2$ gas was successfully stored as hollow vaterite microspheres that have numerous potenti...