  Nuclear structure models built from phenomenological mean fields, the
effective nucleon-nucleon interactions (or Lagrangians), and the realistic bare
nucleon-nucleon interactions are reviewed. The success of covariant density
functional theory (CDFT) to describe nuclear properties and its influence on
Brueckner theory within the relativistic framework are focused upon. The
challenges and ambiguities of predictions for unstable nuclei without data or
for high-density nuclear matter, arising from relativistic density functionals,
are discussed. The basic ideas in building an ab initio relativistic density
functional for nuclear structure from ab initio calculations with realistic
nucleon-nucleon interactions for both nuclear matter and finite nuclei are
presented. The current status of fully self-consistent relativistic
Brueckner-Hartree-Fock (RBHF) calculations for finite nuclei or neutron drops
(ideal systems composed of a finite number of neutrons and confined within an
external field) is reviewed. The guidance and perspectives towards an ab initio
covariant density functional theory for nuclear structure derived from the RBHF
results are provided.

Nuclear Theory;Strongly Correlated Electrons;High Energy Physics - Lattice