In this article, we review the recent theoretical works on the spin fluctuations and superconductivity in iron-based superconductors. Using the fluctuation exchange approximation and multi-orbital tight-binding models, we study the char- acteristics of the spin fluctuations and the symmetries of the superconducting gaps for different iron-based superconductors. We explore the systems with both electron-like and hole-like Fermi surfaces （FS） and the systems with only the electron-like FS. We argue that the spin-fluctuation theories are successful in explaining at least the essential part of the problems, indicating that the spin fluctuation is the common origin of superconductivity in iron-based superconductors.
