Identification of the symmetry of the order parameter (OP) of high-l'c cuprates is important because it helps to understand possible mechanism that govern the physics of these materials. However, up to now, there is no consensus on the symmetry of the OP. On the other hand, nonmagnetic impurity substitutions would test the symmetry of OP. Present theoretical calculations overestimate suppression of the critical temperature (by a factor of 2 or more) in comparison to the experimental data. So far, differences between zinc [Zn) and nickel {Ni) substitutions have not been well understood. Considering the above arguments, effects of nonmagnetic impurities on the high-temperature cuprates are investigated by solving the Bogoliulpv-de Gennes (BdG) equations on two-dimensional square lattice. The critical impurity concentration is found to be very close to the experimental values. Possibility of extracting the symmetry of OP from the obtained results is discussed. Finiteranged impurity potentials and different potential strengths for different impurities are proposed to explain differences between Zn and Ni substitutions. Finally, it is concluded that our results are in favor of d-wave symmetry for tetragonal and s+d-wave symmetry for orthorhombic phase, and explain quite well the effects of nonmagnetic impurity substitutions in the high-7'c oxide superconductors. Beside these, the physical properties of the high-temperature oxide superconductors, the BdG equations and effects of nonmagnetic impurities on isotropic and anisotropic superconductors are reviewed.