  The $\omega$-power of a finitary language L over a finite alphabet $\Sigma$
is the language of infinite words over $\Sigma$ defined by L $\infty$ := {w 0 w
1. .. $\in$ $\Sigma$ $\omega$ | $\forall$i $\in$ $\omega$ w i $\in$ L}. The
$\omega$-powers appear very naturally in Theoretical Computer Science in the
characterization of several classes of languages of infinite words accepted by
various kinds of automata, like B{\"u}chi automata or B{\"u}chi pushdown
automata. We survey some recent results about the links relating Descriptive
Set Theory and $\omega$-powers.
