The study of exotic nuclei---nuclei with the ratio of neutron number $N$ to proton number $Z$ deviating much from that of those found in nature---is at the forefront of nuclear physics research because it can not only reveal novel nuclear properties and thus enrich our knowledge of atomic nuclei, but also help us to understand the origin of chemical elements in the nucleosynthesis. With the development of radioactive ion beam facilities around the world, more and more unstable nuclei become experimentally accessible. Many exotic nuclear phenomena have been observed or predicted in nuclei far from the $\beta$-stability line, such as neutron or proton halos, the shell evolution and changes of nuclear magic numbers, the island of inversion, soft-dipole excitations, clustering effects, new radioactivities, giant neutron halos, the shape decoupling between core and valence nucleons in deformed halo nuclei, etc. In this contribution, I will present a review of theoretical study of exotic nuclear structure. I will first introduce characteristic features and new physics connected with exotic nuclear phenomena: the weakly-bound feature, the large-spatial extension in halo nuclei, deformation effects in halo nuclei, the shell evolution, new radioactivities and clustering effects. Then I will highlight some recent progresses corresponding to these features.