  Relativistic energy density functionals (REDF) provide a complete and
accurate, global description of nuclear structure phenomena. A modern
semi-empirical functional, adjusted to the nuclear matter equation of state and
to empirical masses of deformed nuclei, is applied to studies of shapes of
superheavy nuclei. The theoretical framework is tested in a comparison of
calculated masses, quadrupole deformations, and potential energy barriers to
available data on actinide isotopes. Self-consistent mean-field calculations
predict a variety of spherical, axial and triaxial shapes of long-lived
superheavy nuclei, and their alpha-decay energies and half-lives are compared
to data. A microscopic, REDF-based, quadrupole collective Hamiltonian model is
used to study the effect of explicit treatment of collective correlations in
the calculation of Q{\alpha} values and half-lives.
