Graphene family nanomaterials (GFNs), including graphene, graphene oxide (GO), reduced graphene oxide (rGO), and graphene quantum dots (GQDs), have manifold potential applications, leading to the possibility of their release into environments and the exposure to humans and other organisms. However, the genotoxicity of GFNs on DNA remains largely unknown. In this review, we highlight the interactions between DNA and GFNs and summarize the mechanisms of genotoxicity induced by GFNs. Generally, the genotoxicity can be sub-classified into direct genotoxicity and indirect genotoxicity. The direct genotoxicity (e.g., direct physical nucleus and DNA damage) and indirect genotoxicity mechanisms (e.g., physical destruction, oxidative stress, epigenetic toxicity, and DNA replication) of GFNs were summarized in the manuscript, respectively. Moreover, the influences factors, such as physicochemical properties, exposure dose, and time, on the genotoxicity of GFNs are also briefly discussed. Given the important role of genotoxicity in GFNs exposure risk assessment, future research should be conducted on the following: (1) developing reliable testing methods; (2) elucidating the response mechanisms associated with genotoxicity in depth; and (3) enriching the evaluation database regarding the type of GFNs, applied dosages, and exposure times.