In the last decade, the considerable progress in self-consistent nuclear structure theories based on the density functional concept has shown that they represent a successful strategy toward a universal and precise description of low-energy nuclear dynamics. Driven by fast-progressing disciplines such as astrophysics, experimental studies of exotic nuclear structure, and the synthesis of super-heavy elements, the nuclear density functional theories (DFT) have achieved a level of sophistication that permits descriptions of a wide range of properties for arbitrarily heavy nuclei, including those at the neutron and proton drip lines.

The commonly used density functional theories themselves do not allow for a high-precision description of nuclear properties because of their limited treatment of many-body correlations, which are responsible for the binding of loosely-bound systems, decay properties, and spectra of excitations. Therefore, we include correlations of various types by field theory techniques based on the covariant DFT (CDFT). Thus temporal and spatial non-localities in the in-medium nucleonic interaction allow for the delicate interplay of various kinds of correlations. The Lorentz invariance puts stringent restrictions on the number of parameters in the underlying functional without reducing the quality of agreement with experimental data, and allows for a fully self-consistent and parameter-free implementation of the many-body couplings.

The extended CDFT methodology has provided a very successful description of a wide range of nuclear structure phenomena. Recent developments and perspectives of the extended CDFT are discussed in light of their applications to research topics at radioactive beam facilities, such as NSCL/FRIB, GSI/FAIR, RIKEN/RIBF. Prospects for the extended CDFT in providing a consistent input for astrophysical models aimed at understanding the elemental composition of the universe are also outlined.