  We show that the pushout of an \'etale morphism and an open immersion exists
in the category of algebraic stacks and show that such pushouts behave
similarly to the gluing of two open substacks. For example, quasi-coherent
sheaves on the pushout can be described by a simple gluing procedure. We then
outline a powerful d\'evissage method for representable \'etale morphisms using
such pushouts. We also give a variant of the d\'evissage method for
representable quasi-finite flat morphisms.
