Abstract: In conventional superconductors, Cooper pairs are mediated by phonons, which is a process where only the correlations between the phonons and the charge properties of the electrons are needed. However, so-called unconventional superconductivity can also be derived from other types of elementary excitations.The most promising candidate that can mediate such unconventional superconductivity is spin fluctuations. In some important systems such as cuprates, Fe-based superconductors and certain heavy-fermion superconductors, the spin fluctuations play a key role in understanding the mechanism of their superconductivity although there is still much debate. In this paper we present a brief review of the correlation between spin fluctuations and superconductivity.