Spin and isospin are essential degrees of freedom in nuclear systems, and the relevant studies on their properties play important roles not only in nuclear physics but also in nuclear astrophysics, particle physics, and so on. In this presentation for the IUPAP Young Scientist Prize 2016, I would like to introduce the microscopic studies on nuclear spin-isospin properties in the framework of covariant density functional theory (DFT), by taking a few works that I have been joining in as examples. It is seen that the covariant scheme plays an important role in describing the spin properties in a consistent way, such as the spin-orbit splitting, the pseudospin symmetry, etc. Meanwhile, the Fock terms play important roles in describing the isospin properties fully self-consistently, such as the Gamow-Teller and spin-dipole resonances, the isospin-symmetry-breaking corrections to nuclear superallowed $\beta$ transitions, etc. To connect the covariant DFT to more fundamental theories, an \textit{ab initio} relativistic Brueckner-Hartree-Fock theory for finite nuclei is introduced, and a personal perspective for the coming decade is also illustrated.