Covariant [relativistic] density functional theory (CDFT), the basic features of which will be introduced in the beginning of my talk, is well established theoretical tool for the description of nuclear systems. However, there are still a number of important topics which have not been either addressed or satisfactorily resolved within its framework. In my talk, I will concentrate on one of them, namely, on single-particle motion. For a long period of time, CDFT has been applied mostly to collective phenomena and only recently the interest has shifted to the description of the single-particle motion in nuclear systems. The successes and limitations of the description of single-particle degrees of freedom in spherical, deformed and rotating nuclei within the CDFT will be discussed. Further improvement of the description of the energies of predominantly single-particle states and their wave functions requires beyond mean field methods built on CDFT which include particle-vibration coupling. The impact of particle-vibration coupling on different physical observables such as the energies of predominantly single-particle states, the spin-orbit splittings, the energy splittings in pseudospin doublets will be illustrated in spherical nuclei ranging from light up to superheavy ones. I will also compare the description of these degrees of freedom in nuclear and non-nuclear density functional theories.