  We give an explicit description of the irreducible components of the moduli
spaces of polarized Enriques surfaces in terms of decompositions of the
polarization as an effective sum of isotropic classes. We prove that infinitely
many of these components are unirational (resp. uniruled). In particular, this
applies to components of arbitrarily large genus $g$ and $\phi$-invariant of
the polarization.
