The chapter gives an overview of the main approaches formulated to model interlaminar damage and imperfections in layered structures using zigzag kinematic approximations and concentrates on the models which have been extended to analyze delamination damage progression. The zigzag theories are structural theories which assume different kinematic fields in the layers, to account for zigzag effects associated to their elastic mismatch, and use a fixed number of variables that is independent of the number of layers. Interfacial imperfections, interlayer damage, and delaminations are included using the compliant layer concept, imperfect interfaces, or by adding additional variables.