  In this short review, I discuss basic qualitative characteristics of quantum
non-Abelian gauge dynamics in the non-stationary background of the expanding
Universe in the framework of the standard Einstein--Yang--Mills formulation. A
brief outlook of existing studies of cosmological Yang--Mills fields and their
properties will be given. Quantum effects have a profound impact on the gauge
field-driven cosmological evolution. In particular, a dynamical formation of
the spatially-homogeneous and isotropic gauge field condensate may be
responsible for both early and late-time acceleration, as well as for dynamical
compensation of non-perturbative quantum vacua contributions to the ground
state of the Universe. The main properties of such a condensate in the
effective QCD theory at the flat Friedmann--Lema\'itre--Robertson--Walker
(FLRW) background will be discussed within and beyond perturbation theory.
Finally, a phenomenologically consistent dark energy can be induced dynamically
as a remnant of the QCD vacua compensation arising from leading-order
graviton-mediated corrections to the QCD ground state.
