We review the progress of nonmagnetic impurity doping study on the Fe-based superconductors.On the theoretical side, two highly potential candidates for the pairing symmetry order parameter, i.e. the multi-gap s++ and s± wave models, have been proposed but continuously debated. The debate arises because of the complex gap structure, exceptive magnetic and metallic behaviors of Fe-based superconductors which may make the influences of nonmagnetic defects varied in chemical potential, impurity disorder, inter-and intra-band scattering strength, and electron localization, and hence difficulty in directly obtaining the most important information for understanding the symmetry order parameter. Experimentally, the nonmagnetic impurity substitution study has been widely carried out, which has provided very useful insights. We review herein the various nonmagnetic impurity doping experiments, including the controlled defects within the superconducting Fe2X2 planes through samples quality improvement, a single impurity effects on the electronic state and local moment, the magnetic response of the Fe2X2 planes both on macroscopic scale as antiferromagnetic state and local scale of moment, as well as the significant effect in modifying the transport properties. The experiments enable us to qualitatively analyze the nonmagnetic impurities effects on the superconducting state for many Fe-based superconductors. We also propose herein some strategies for the nonmagnetic impurity doping study. As an important model for explaining the nonmagnetic impurities doping effects, the pair-breaking model is compared with various theoretical approaches via analyzing the pair-breaking rates of various Fe-superconductors.