This work sheds light upon how the atomic nucleus polarizes throughout the nuclear chart. Deviations from the well-known behavior of the nuclear dipole polarizability — which smoothly increases with increasing atomic mass number — are investigated. Relative enhancements are found for light nuclei as the nuclear symmetry energy decreases and, within a nucleus, as its excitation energy increases. These two properties are related by a diminishing binding energy of the nuclear system. Contrarily, hindrances of nuclear polarizability are observed in the photo-neutron cross-section data and photon-strength functions of semi-magic nuclei with [Formula: see text], 50 and 82, which support the presence of shell effects at low-lying excitations and — assuming validity of the Brink-Axel hypothesis — at high-excitation energies up to the quasi-continuum region. These features assign the nuclear dipole polarizability as a sensitive measure of the long-range correlations of the nuclear force, and provide a new spectroscopic probe to investigate collective phenomena, shell closures, and the elusive nuclear symmetry energy. Particular cases of quadrupole collectivity are also discussed in terms of the available, and yet so scarce, information on nuclear polarizability (e.g. Sn and Ni isotopes).