  As indicated by Einstein's general relativity, matter and geometry are two
faces of a single nature. In our point of view, extra dimensions, as a member
of the {\em geometry face}, will be treated as a part of the {\em matter face}
when they are beyond our poor vision, thereby providing dark energy sources
effectively. The geometrical structure and the evolution pattern of extra
dimensions therefore may play an important role in cosmology. Various possible
impacts of extra dimensions on cosmology are investigated. In one way, the
evolution of homogeneous extra dimensions may contribute to dark energy,
driving the accelerating expansion of the universe. In the other way, both the
energy perturbations in the ordinary three-space, combined with homogeneous
extra dimensions, and the inhomogeneities in the extra space may contribute to
dark matter. In this paper we wish to sketch the basic idea and show how extra
dimensions may lead to the dark side of our universe.
