  Here we focus on the compactification of the moduli space of curves of genus
g together with an unramified double cover, constructed by Arnaud Beauville in
order to compactify the Prym mapping. We present an alternative description of
it, inspired by the moduli space of spin curves of Maurizio Cornalba, and we
discuss in detail its main features, both from a geometrical and a
combinatorial point of view.
