  We discuss cosmology of models with universal extra dimensions, where the
Standard Model degrees of freedom live in a $4+n$ dimensional brane, with $n$
compact and small extra spatial dimensions. In these models, the simplest way
to obtain the conventional 4-dimensional Planck scale starting with a low
string scale is to have also some larger extra dimensions, where only gravity
propagates. In such theories, dimensional reduction generically leads to at
least two radion fields, one associated with the total volume of the extra
spatial dimensions, and the other with the ratio of the sizes of small and
large extra dimensions. In this paper, we discuss the impact of the radion
fields on cosmology. We emphasize various aspects of radion physics such as
radion coupling to the Standard Model fields, bare and dressed radion masses
during inflation, dynamical stabilization of radions during and after
inflation, radion decay life time and its late dominance in thermal history of
the Universe as well as its quantum fluctuations during inflation. We argue
that models where the radion plays the role of an inflaton or the inflaton is a
brane scalar field, run into problems. We then present a successful inflation
model with bulk scalar fields that seems to have all the desired properties. We
also briefly discuss the possibility of radion as a cold dark matter candidate.
