The paper by Vogt, Moch, and Vermaseren calculates the next-to-next-to-leading order (NNLO) contributions to the splitting functions governing the evolution of unpolarized flavor-singlet parton densities in perturbative QCD. The exact expressions are presented in both Mellin-$N$ and Bjorken-$x$ spaces, and accurate parametrizations are provided for practical applications. The results agree with all partial findings in the literature. The leading logarithmic predictions for small momentum fractions $x$ do not provide good estimates of the complete splitting functions. The corrections are investigated, and the stability of the NNLO evolution under variation of the renormalization scale is studied. The perturbative expansion converges rapidly for $x \gtrsim 10^{-3}$, while relatively large third-order corrections are found at smaller values of $x$.The paper by Vogt, Moch, and Vermaseren calculates the next-to-next-to-leading order (NNLO) contributions to the splitting functions governing the evolution of unpolarized flavor-singlet parton densities in perturbative QCD. The exact expressions are presented in both Mellin-$N$ and Bjorken-$x$ spaces, and accurate parametrizations are provided for practical applications. The results agree with all partial findings in the literature. The leading logarithmic predictions for small momentum fractions $x$ do not provide good estimates of the complete splitting functions. The corrections are investigated, and the stability of the NNLO evolution under variation of the renormalization scale is studied. The perturbative expansion converges rapidly for $x \gtrsim 10^{-3}$, while relatively large third-order corrections are found at smaller values of $x$.