Two relativistic approaches are considered to evaluate the quasielastic double-differential and integrated neutrino-nucleus cross sections. One, based on the relativistic impulse approximation, relies on the relativistic Fermi gas model. The other, based on the relativistic mean field model, uses a more realistic description of the nuclear structure. The results are compared with the non-relativistic impulse approximation and the relativistic mean field model. The relativistic approaches provide a more accurate description of the quasielastic neutrino-nucleus cross sections, especially at high energies.