  We review cosmology in non-minimal Yang-Mills/Maxwell theory, in which the
Yang-Mills/electromagnetic field couples to a function of the scalar curvature.
We show that power-law inflation can be realized due to the non-minimal
gravitational coupling of the Yang-Mills field which may be caused by quantum
corrections. Moreover, we study non-minimal vector model in the framework of
modified gravity and demonstrate that both inflation and the late-time
accelerated expansion of the universe can be realized. We also discuss the
cosmological reconstruction of the Yang-Mills theory. Furthermore, we
investigate late-time cosmology in non-minimal Maxwell-Einstein theory. We
explore the forms of the non-minimal gravitational coupling which generate the
finite-time future singularities and the general conditions for this coupling
in order that the finite-time future singularities cannot appear.
