The occurrence of a bifurcation in a multilayer structure during loading sets a limit on its deformability, and therefore represents an important factor in the design of composites. Since bifurcationis strongly influenced by the contact conditions at the interfaces between the layers, the mechanical modeling of these conditions is crucial. The theory of incremental bifurcation is reviewed for elastic multilayers, when these are subject to a finite strain before bifurcation, corresponding to uniform tension/compression and finite bending. The interlaminar contact is described by introducing linear imperfect interfaces. Results are critically discussed in view of applications and available experiments.