  We give a simultaneous generalization of recollements of abelian categories
and triangulated categories, which we call recollements of extriangulated
categories. For a recollement $(\mathcal{A}$, $\mathcal{B}$, $\mathcal{C})$ of
extriangulated categories, we show that cotorsion pairs in $\mathcal{A}$ and
$\mathcal{C}$ induce cotorsion pairs in $\mathcal{B}$ under certain conditions.
As an application, our main result recovers a result given by Chen for
recollements of triangulated categories, and it also shows a new phenomena when
it is applied to abelian categories.
