Descent data, in general, should be expressed in terms of a homotopy limit. In this talk we study the homotopy limits of some cosimplicial diagrams of dg-categories which arise in algebra and geometry: the homotopy limits are explicitly given by twisted complexes. In particular our construction works in the following two cases: (1) the complexes of sheaves on the Cech nerve of an open cover of a scheme; (2) the complexes of sheaves on the simplicial nerve of a discrete group acting on a scheme. The result can be applied in the study of descent theory of dg-categories and equivariant dg-categories. This is a joint work in progress with Jonathan Block and Julian Holstein.