Fluorination can significantly change the physical and chemical properties of carbon materials (CMs). Common sense for the fluorination mechanism for CMs indicates that one basal-plane C-F group (CF group) can form as one fluorine atom bonded to one carbon atom along the out-of-plane carbon networks without creating edge C-F groups (including CF2 and CF3 groups) at vacancies in carbon networks. We report that fluorination can generally create edge C-F groups in multidimensional CMs such as graphite, graphene, carbon nanotubes, and fullerene, and the concentration of edge C-F groups is dependent on both the crystallinity of starting CMs and the fluorination pressure and temperature. As an example, we show the significant differences in the band gap opening, photoluminescence, and magnetic properties between two half-fluorinated graphenes with different concentrations of edge C-F groups. Our findings highlight the importance of fluorination in creating edge C-F groups in the structure and properties and introduce new insight into fluorinated CMs.