  On construit les champs de Hurwitz et on en donne quelques propri\'et\'es,
essentiellement contenues dans SGA 1. Quelques applications de nature
arithm\'etique en sont d\'eduites.
  We propose a construction of Hurwitz stacks and give some properties of them,
most of which are consequences of SGA 1. Some applications of arithmetic flavor
are then deduced.
