Currently, there is strong interest in the effects of impact induced damage to composite structures as evidenced by the large number of articles on this topic that have appeared in the literature in recent years. With laminated composite structures, foreign object impacts, that are expected to occur during the life of the structure, can introduce damage that is often difficult to detect and can significantly reduce the strength of the structure. Research efforts concentrate on monolithic laminates while sandwich structures with laminated facings, which are also used extensively in aerospace and other applications, received less attention. A comprehensive review of the literature dealing with impact on sandwich structures is presented in this review article. The mechanics of contact between a rigid indentor and a sandwich structure is discussed in detail since it is very important to account for the local deformation in the contact zone in developing a model for predicting the contact force history. The mechanical behavior of foam and honeycomb core materials is reviewed along with experimental results and models for predicting the contact law between a smooth indentor and a sandwich structure. The development of mathematical models for predicting the contact force history and the overall response of the structure is also discussed. Finally we review the failure mechanisms involved in impact damage development, the parameters affecting damage size, and the residual properties of sandwich structures. This review article has 85 references.