The propagation of cracks in model glass/epoxy structures from low-velocity impact by a sharp or spherical projectile is observed in real time with the aid of a high-speed camera. Tests are also carried out to determine the threshold impact energy for chipping in a glass block and subsurface crack instability in a glass plate. Fracture may occur by a number of mechanisms including cone cracks and median-radial cracks initiating from the impact site or radial cracks initiating from the subsurface of the plate. The results identify the median-radial crack as a potent damage source in such applications. The equation of motion of a mass impacting a flat-surface target is solved analytically under the assumption of quasistatic load transfer between projectile and target and taking into consideration contact and flexural deformations as well as plastic penetration of the tool into the material. The growth history of the median crack is then found using an appropriate relationship between crack length and contact load. The predicted threshold impact energy for chipping or flexure-induced crack instability compare well with the experiments. The analysis explicitly exposes the role of projectile's bluntness, mass, and velocity as well as the target stiffness, toughness and hardness on damage tolerance of layered structures.