The paper discusses the application of generalized gradient approximations (GGAs) to improve the accuracy of electronic structure calculations. The authors focus on the Perdew-Wang (PW) GGA, which is based on real-space cutoffs of the spurious long-range components in the second-order gradient expansion for the exchange-correlation hole. The PW GGA is tested against various physical systems, including atoms, molecules, solids, and surfaces. The results show that the PW GGA significantly improves the accuracy of total energies, ionization energies, electron affinities, and atomization energies compared to the local-spin-density (LSD) approximation. The PW GGA also corrects the underestimation of lattice constants in lithium and sodium and restores the magnetic ground state in solid iron. For surfaces, the PW GGA reduces the work function, surface energy, and curvature energy compared to LSD, and includes a long-range correction to the surface energy. The paper also explores the cancellation of errors between density functionals for exchange and correlation, which is most pronounced when the Hartree-Fock result is furthest from experimental values. Overall, the PW GGA provides a more accurate and reliable description of electronic structure for a wide range of systems.The paper discusses the application of generalized gradient approximations (GGAs) to improve the accuracy of electronic structure calculations. The authors focus on the Perdew-Wang (PW) GGA, which is based on real-space cutoffs of the spurious long-range components in the second-order gradient expansion for the exchange-correlation hole. The PW GGA is tested against various physical systems, including atoms, molecules, solids, and surfaces. The results show that the PW GGA significantly improves the accuracy of total energies, ionization energies, electron affinities, and atomization energies compared to the local-spin-density (LSD) approximation. The PW GGA also corrects the underestimation of lattice constants in lithium and sodium and restores the magnetic ground state in solid iron. For surfaces, the PW GGA reduces the work function, surface energy, and curvature energy compared to LSD, and includes a long-range correction to the surface energy. The paper also explores the cancellation of errors between density functionals for exchange and correlation, which is most pronounced when the Hartree-Fock result is furthest from experimental values. Overall, the PW GGA provides a more accurate and reliable description of electronic structure for a wide range of systems.