We review the progress of nonmagnetic impurity doping studies on Fe-based superconductors. On the theoretical side, two highly promising 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 and exceptional magnetic and metallic behaviors of Fe-based superconductors, which may vary the influence of nonmagnetic defects in the chemical potential, impurity disorder, inter- and intra-band scattering strength, and electron localization. This creates difficulties in directly obtaining the most important information for understanding the symmetry order parameter. Experimentally, nonmagnetic impurity substitution studies have been widely carried out, which have provided very useful insights. We review herein the various nonmagnetic impurity doping experiments, including the controlled defects within the superconducting Fe2X2 planes through sample quality improvement, single impurity effects on the electronic state and local moment, the magnetic response of the Fe2X2 planes both on the macroscopic scale as the antiferromagnetic state and the local scale of moment, as well as the significant effect of modifying the transport properties. The experiments enable us to qualitatively analyze the nonmagnetic impurity effects on the superconducting state for many Fe-based superconductors. We also propose herein some strategies for nonmagnetic impurity doping study. As an important model for explaining the nonmagnetic impurity doping effects, the pair-breaking model is compared with various theoretical approaches via analysis of the pair-breaking rates of various Fe-superconductors. [ABSTRACT FROM AUTHOR]