The article is a review of the development of Wigner’sSU(4) description of different nuclear phenomena. It includes descriptions of the collective isospin, spin and spin-isospin states and charge exchange reactions in terms of Wigner’s symmetry. By using microscopic schemes we demonstrate that one can useSU(4) terms both in the deformed and spherical nuclei for special types of collective states: Analogue and Gamow-Teller Resonances, in the charged excitation branch, independently of whether the basic coupling schemes of the nucleons are ofjj orLS type. However the situation in the neutral excitation branch is quite different. For the deformed nuclei one can useSU(4) terms for the description ofM1-transitions in terms of the perturbation effect of spin-orbital forces. For the spherical onesM1-collective states should be described in terms of a brokenSU(4) symmetry as a consequence of great spin-orbit forces and non-saturation of the spin degree of freedom at the line of nuclear stability, even in “magic” nuclei. Simple examples of the use ofSU(4) symmetry for nuclear charge exchange reactions with phenomenological theories are also demonstrated.