The third-order nonlinear effect in optical fiber can be used to prepare a variety of quantum states, which provides an effective tool for the study of quantum information. Because of the long interacting length and low transmission loss, the waveguide structure of optical fibers can significantly enhance the nonlinear effects. On the other hand, the quantum states originate from the waveguide have a well-defined pure spatial mode, which is helpful for the collection and manipulation of the quantum states. Moreover, the commercially available fiber components are mature, effective, and low-priced. Therefore, there is a prospect of developing all fiber quantum light sources, which are not only miniaturized and low-cost, but also compatible with the optical fiber network. In this paper, we review the generation of quantum correlated photon pairs in different kinds of optical fibers, including the photon pairs in different wavelength bands and with different spectral properties, and entangled photon pairs in different degrees of freedoms.