  We present some applications of the Macaulay2 software package
SpecialFanoFourfolds, a package for working with Hodge-special cubic fourfolds
and Hodge-special Gushel--Mukai fourfolds. In particular, we show how to
construct new examples of such fourfolds, some of which turn out to be
rational. We also describe how to calculate K3 surfaces associated with cubic
or Gushel-Mukai fourfolds, which relies on an explicit unirationality of some
moduli spaces of K3 surfaces.
