The development of worldwide rare isotope beam facilities has brought many new insights in nuclear physics. In particular, novel structure in nuclei towards extreme isospin and spin has acquired great interest over the years for the challenges and implications it involves. Theoretically, covariant density functional theory (CDFT) has achieved great success in describing many nuclear phenomena over the past several decades. In this talk, I will highlight recent progress in improving and extending the nuclear CDFT, which are motivated by experimental results on both nuclear ground and excited states. We developed a new covariant functional PC-PK1, which considerably improves the isospin dependence of nuclear properties, and is more reliable for the description of neutron-rich nuclei. We also extended CDFT for nuclear spectroscopic properties within the tilted-axis-cranking approach. It has provided successful description of novel rotation and exotic shape for nuclei towards high isospin and spin. The success of our model stimulates a number of new measurements, and I will present several examples for our interactive research with experimentalists.