Abstract: Relativistic Brueckner-Hartree-Fock(RBHF) theory is one of the most important ab initio methods in the relativistic framework, where the saturation properties of nuclear matter could be described satisfactorily with only considering two-body forces. By achieving the self-consistent solution of the RBHF equations for nuclear matter in the full Dirac space, the scalar and vector components of the single-particle potential have been determined uniquely, the uncertainties caused by the neglect of negative-energy states(NESs) have been avoided, and the long-standing problem over 40 years of not being able to uniquely determine the single-particle potential has been solved. The history of the RBHF theory is briefly reviewed, and the necessity of considering NESs is illustrated. The latest results of nuclear matter and neutron star matter by the RBHF theory in the full Dirac space are discussed, including the effective mass, the binding energy per particle of pure neutron matter, the pressure of symmetric nuclear matter and pure neutron matter, the particle fractions as well as the equation of state for neutron star matter, and the mass-radius relation as well as the tidal deformability of a neutron star. Possible applications of the RBHF theory in the full Dirac space are also discussed, including the calibration of the parameters in density functional theory, the microscopic description of nucleon-nucleus elastic scattering, and the research on the hadron-quark transition inside neutron stars.