Results related to the buckling delamination of elastic and viscoelastic composite plates are reviewed and analyzed. They have been obtained during the last fifteen years by the author and his students. The plates contain cracks whose faces have initial infinitesimal imperfections. The evolution of the imperfections under compression of the plates is studied, and the values of critical parameters are determined from a criterion of initial imperfection. The study is performed with the use of 3D geometrically nonlinear field equations. In the present paper, the historical background of the problems is outlined considered, general remarks about the field equations and solution method are made, and problems related to the plane strain state are reviewed.