Click chemistry has been widely applied to the functionalization of graphene due to its special properties of easy process, flexibility and high efficiency. In this paper, we have present a detailed review of the functionalization of graphene and graphene oxide via click chemistry. The functionalization methods through click chemistry can be divided into two main strategies of the covalent functionalization and the non-covalent functionalization. In addition, the former is further discussed in term of chemical bonds formed on the edge of graphene and chemical bonds formed on the surface of graphene via click chemistry. First, we provide a detailed classification and summary of the reaction process, condition and characterization of the functionalization through click chemistry. On the one hand, according to the position where the click chemistry takes place, the clicking functionalization of graphene can be classified into click reaction on the edge of the graphene oxide, click reaction on the surface of the graphene oxide, click reaction on the surface of the graphene, Diels-Alder[4+2] click reaction on the surface of the graphene, and click chemistry via π-π non-covalent functionalization. Moreover, we have presented and discussed significant research references related to the above five parts. On the other hand, the synthetic routes including the linking methods, click reaction conditions, reaction conditions of the alkynylation and azido functionalization of the graphene, graphene oxide, and the corresponding reactants have been summarized and listed. In addition, the functional properties and the potential applications of the functionalized graphene and graphene oxide are also concluded. To further clearly illustrate and make a summary of the functionalization method of graphene and graphene oxide via click chemistry in details, a table is listed and shown in the paper. Furthermore, we have elaborate the common characterizations methods including IR, Raman, UV, 1H NMR, 13C NMR, XPS, XRD, AFM, TEM, SEM, CV, TGA, and the common characterization results are analyzed and briefly discussed. At last, the potential application of click chemistry on the functionalization of graphene and graphene oxide was summarized.