Covalent functionalization of the surface is more crucial in 2D materials than in conventional bulk materials because of their atomic thinness, large surface-to-volume ratio, and uniform surface chemical potential. Because 2D materials are composed of two surfaces with no dangling bond, covalent functionalization enables us to improve or precisely modify the electrical, mechanical, and chemical properties. In this review, we summarize the covalent functionalization methods and related changes in properties. First, we discuss possible sites for functionalization. Consequently, functionalization techniques are introduced, followed by the direct synthesis of functionalized 2D materials and characterization methods of functionalized 2D materials. Finally, we suggest how the issues may be solved to enlarge the research area and understanding of the chemistry of 2D materials. This review will help in understanding the functionalization of 2D materials.