Study of low-velocity impact (LVI) performance of fabric reinforced polymer (FRP) composites has drawn keen interest from the research community due to its application in various fields. In this direction material designers and scientists have reported the behavior and performance of advanced composites subjected to LVI. In this paper the existing literature and current research relating to LVI behavior and performance of fabric reinforced polymer composites and nanocomposites are briefly reviewed. The impact behavior of some representative fabric reinforcements such as glass, carbon, Kevlar, Twaron, and hybrid fabric reinforcements in different matrix formulations have been discussed. The effect of fabric hybridization and nanofiller incorporation has also been reviewed. The fabrication methods, process parameters to achieve LVI application-centric fabric reinforced polymer composites and their characterization methods and testing standards are reported. Also, the failure mechanisms observed in FRP composites when subjected to LVI events are briefly discussed. Such information relating to LVI resistant polymer composite materials has significant implications in the development of advanced composite systems and to achieve material sufficiency for a wide range of structural applications.