We give a short account of recent advances in our understanding of the π- dependent terms in massless (Euclidean) 2-point functions as well as in generic anomalous dimensions (ADs) and β-functions. We extend the considerations of  by two more loops, that is for the case of 6- and 7-loop correlators and 7- and 8-loop renormalization group (RG) functions. Our predictions for the (π-dependent terms) of the 7-loop RG functions for the case of the O(n) 𝜙4 theory are in full agreement with the recent results from . All available 7- and 8-loop results for QCD and the scalar O(n) ϕ4 theory obtained within the large Nf approach to the quantum field theory (see, e.g. ) are also in full agreement with our results.