An application of some modern methods to studying cracks in aligned composites and an interaction of curvilinear cracks with an interface is presented. The first method based on Novozhilov's hybrid model is focused on estimation of variation intervals of sizes of a partially bridged equilibrium crack and bridging zone. The problem of a slightly curved crack near an interface is solved by a combination of some methods which are Muskhelishvili's method of complex potentials, an original superposition method reduced to Fredholm integral equations of the second type, and a boundary perturbation method.