We give a simultaneous generalization of recollements of abelian categories and triangulated categories, which we call recollements of extriangulated categories. For a recollement (A, B, C) of extriangulated categories, we show that cotorsion pairs in A and C induce cotorsion pairs in B
Nearby in the stack
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.