Hybrid nanostructures composed of graphene or other two-dimensional (2D) nanomaterials and plasmonic metal components have been extensively studied. The unusual properties of 2D materials are associated with their atomically thin thickness and 2D morphology, and many impressive structures enable the metal nanomaterials to establish various interesting hybrid nanostructures with outstanding plasmonic properties. In addition, the hybrid nanostructures display unique optical characteristics that are derived from the close conjunction of plasmonic optical effects and the unique physicochemical properties of 2D materials. More importantly, the hybrid nanostructures show several plasmonic electrical effects including an improved photogeneration rate, efficient carrier transfer, and a plasmon-induced "hot carrier", playing a significant role in enhancing device performance. They have been widely studied for plasmon-enhanced optical signals, photocatalysis, photodetectors (PDs), and solar cells. In this review, the developments in the field of metal/2D hybrid nanostructures are comprehensively described. Preparation of hybrid nanostructures is first presented according to the 2D material type, as well as the metal nanomaterial morphology. The plasmonic properties and the enabled applications of the hybrid nanostructures are then described. Lastly, possible future research in this promising field is discussed.