  It is commonly assumed that the energy density of the Universe was dominated
by radiation between reheating after inflation and the onset of matter
domination 54,000 years later. While the abundance of light elements indicates
that the Universe was radiation dominated during Big Bang Nucleosynthesis
(BBN), there is scant evidence that the Universe was radiation dominated prior
to BBN. It is therefore possible that the cosmological history was more
complicated, with deviations from the standard radiation domination during the
earliest epochs. Indeed, several interesting proposals regarding various topics
such as the generation of dark matter, matter-antimatter asymmetry,
gravitational waves, primordial black holes, or microhalos during a nonstandard
expansion phase have been recently made. In this paper, we review various
possible causes and consequences of deviations from radiation domination in the
early Universe - taking place either before or after BBN - and the constraints
on them, as they have been discussed in the literature during the recent years.
