The ω-power of a finitary language L over a finite alphabet Σ is the language of infinite words over Σ defined by L ∞ := {w 0 w 1. .. ∈ Σ ω | ∀i ∈ ω w i ∈ L}. The ω-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 Büchi automata or Büchi pushdown automata. We survey some recent results about the links relating Descriptive Set Theory and ω-powers.