Spin fluctuations and uncoventional superconducting pairing

High-<i>T</i>_c cuprates, iron-based superconductors, heavy-fermion superconductors and <i>κ</i>-type layered organic superconductors share some common features − the proximity of the superconducting state to the magnetic ordered state and the non-<i>s</i>-wave superconducting pairing function. It is generally believed that the Cooper pairings in these unconventional superconductors are mediated by spin fluctuations. In this paper, we present a brief overview on the spin dynamics and unconventional pairing, focusing on high-<i>T</i>_c cuprates and iron-based superconductors. In particular, we will overview the properties of the neutron spin resonance and its possible origin, the pairing mechanism in Hubbard model within the weak-coupling framework and its application to the aforesaid unconventional superconductors. We point out that the interplay between magnetism and superconductivity is still an area of active research.