A comprehensive Car-Parrinello molecular dynamics (CP-MD) study of aqueous solutions of carbonic acid (H2CO3) bicarbonate (HCO3-) carbonate (CO32-) and carbon dioxide (CO2) provides new quantitative insight into the structural and dynamic aspects of the hydrogen-bonding environments for these important aqueous species and their effects on the structure, H-bonding, and dynamical behavior of the surrounding water molecules. The hydration structures of the different carbonate species depend on their ability to accept and donate H-bonds with H2O. The H-bonds donated by the C-O-H sites of the carbonate species to water molecules are generally stronger and longer-lived than those accepted by these sites from water molecules. The structural relaxation among the water molecules is dominated by diffusional (translational) motion of H2O, whereas the H-bond reorganization is dominated by the librational motion of the water molecules and the carbonate species. The rates of structural relaxation of the H2O molecules and the rates of H-bond reorganization among them are slower in systems containing carbonate species, consistent with previous studies of simple salt solutions. The strengths and lifetimes of H-bonds involving the carbonate species positively correlate with the total negative charge on the species. H-bond donation from H2O to CO2 is weak, but the presence of CO2 noticeably affects the structure and structural relaxation of the surrounding H-bonding network leading to generally stronger H-bonds and slower relaxation rates, the behavior typical of a hydrophobic solute.