  A diagram of groupoid correspondences is a homomorphism to the bicategory of
\'etale groupoid correspondences. We study examples of such diagrams, including
complexes of groups and self-similar higher-rank graphs. We encode the diagram
in a single groupoid, which we call its groupoid model. The groupoid model is
defined so that there is a natural bijection between its actions on a space and
suitably defined actions of the diagram. We describe the groupoid model in
several cases, including a complex of groups or a self-similar group. We show
that the groupoid model is a bilimit in the bicategory of groupoid
correspondences.
