Covariant density functional theory (CDFT) has achieved great success in describing many nuclear phenomena over the past several decades. I will present our recent works on the improvement of the energy density functional as well as several applications of CDFT that have been motivated by recent experimental results on both nuclear ground states and rotational excitation states. It is found that the new energy density functional PC-PK1 provides great improvement for the isospin-dependence properties, which makes it more reliable for the neutron-rich exotic nuclei. With the extension of tilted axis cranking approach, the CDFT has also been successfully applied to describe the novel phenomena of magnetic and antimagnetic rotation in a self-consistent and microscopic way. Finally, the very recent work on projected shell model calculations beyond CDFT will be briefly discussed.