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We review the status and precision of evolution equations for parton
distribution functions (PDFs) in QCD.
We present ongoing efforts on extending the evolution kernels and
splitting functions to four loop accuracy in the perturbative expansion.
We discuss the impact on determination of of PDFs, the strong coupling and
the heavy quark masses in global fits of data from the LHC as well as the
combined data from for inclusive deep-inelastic scattering.
We illustrate how the precision of available experimental data challenges
current theoretical predictions and we outline areas for future
improvements.