Calculations of Feynman graphs up to five loops in perturbative QCD are currently available for several observables. The knowledge of the higher-order perturbative coefficients is of interest for precision tests of the Standard Model, especially at intermediate energies. However, exact higher-loop calculations are not expected in the near future due to huge computational difficulties. In this talk, after a brief review of recent developments in perturbative QCD inspired from mathematical ideas of transseries and resurgence, I present a determination of the perturbative coefficients of the QCD Adler function up to eight-loop order using the method of conformal mappings of the Borel plane. I argue also that the perturbative expansions improved by conformal mappings may represent an alternative to transseries in recovering the exact function.