This manuscript investigates compression-after-impact failure in woven fiber-reinforced composites. Compression failure of composite structures previously damaged by an impact event is due to the propagation of impact-induced damage mechanisms such as interlaminar debonding, constituent (i.e., matrix and fiber) microcracking, sublaminate buckling, as well as the interactions between these mechanisms. The failure mechanisms within each ply are idealized based on a reduced order multiscale computational model, in which, the damage propagation in the matrix and fibers upon compression is explicitly modeled. Delamination along the ply interfaces is idealized using a cohesive surface model. The initial impact-induced damage within the microconstituents and interfaces are inferred from experimental observations. A suite of numerical simulations is conducted to understand the sublaminate buckling, propagation of delamination and constituent damage upon compression loading. The numerical investigations suggest extensive propagation of delamination with mode transition preceding sublaminate buckling. Initiation and propagation of matrix and fiber cracking, observed upon sublaminate buckling, is the cause of ultimate shear failure.