I present analytic results for the scale evolution of the ten lowest moments of the Parton Distribution Functions (PDFs) through four loops in QCD. I discuss the evolution of the PDFs to approximate N${}^{3}$LO accuracy, which is obtained by combining input from the computed moments and from physical constraints. The contribution to the scale evolution of the PDFs of the approximate N${}^{3}$LO corrections is of the order of $1\%$ or less for $x\gtrsim10^{-4}$. The uncertainty of the approximations is estimated below $1\%$ for $x\gtrsim 10^{-4}$, thus they are relevant for precision phenomenology at the LHC.