Modern methods for the description of the nuclear many-body system use the concepts of density functional theory (DFT) and of effective field theory (EFT). The covariant version of this theory is based on a density functional which takes into account Lorentz symmetry in a self-consistent way. Pairing correlations play an important role in all open-shell configurations. They are included in relativistic Hartree Bogoliubov (RHB) theory by an effective residual interaction of finite range. With a minimal number of parameters this theory allows a very successful phenomenological description of ground state properties of nuclei all over the periodic table. Recently this method has also been applied for the description of very heavy and super-heavy elements.