In this talk I would like to give a general introduction to the theoretical framework of the so-called shell-model configuration interaction approach. I will show how the effective interaction can be constructed starting from the realistic nucleon-nucleon interaction and how the theoretical results can be compared with experimental data. Then I will introduce the nuclear pairing and quadrupole-qaudrupole correlations and their indication on the symmetry properties on the many-body wave function. In particular, the seniority symmetry manifests itself in semi-magic nuclei where pairing correlation dominates. As examples, I will introduce our recent studies regarding the seniority structure of nuclei around the doubly-magic 100Sn and 208Pb. In particular, I will show that the seniority symmetry is dynamically conserved in j=9/2 shells irrespective of type of interaction. This may be a unique phenomenon for nuclear physics, which is characterized by large spin-orbit coupling. Moreover, I will show that proton-neutron pair coupling can favoured when both proton and neutron degrees of freedom are relevant. I will then discuss the collectivity properties in Sn and Te isotopes and the possible role played by the cross-shell excitation and the quadrupole-quadrupole correlation. The effect of such coupling on alpha and other decay properties will also be discussed.