Sandwich composite structures have been extensively used in the aviation industry thanks to their low weight and superior mechanical properties. As they are generally employed as structural components, sustaining their structural integrity under various loading conditions is crucial. Impact loading is one of the critical loading types that such materials may be exposed to in service. Their response to impact loading and their post-impact behavior depend on various parameters related to their manufacturing. Assessment of impact resistance of sandwich composite materials during the design process can be challenging. In this review, the previous studies focused on the parameters affecting the impact behavior of composite sandwich structures are examined in detail. Analysis of these studies can significantly improve the design process. The main type of sandwich materials investigated in this review is composed of aluminum, glass/carbon/kevlar-fiber-reinforced polymer facesheets and Nomex®/Aluminum honeycomb or foam core material based on their wide use in the aviation industry. The focus is on the past efforts aimed at the understanding of impact behavior of sandwich structures; some suggestions for the future studies are also provided.