The ideal graphene is a one-atom thick single layer of carbon atoms having sp hybridation in hexagonal arrangement. Due to their large surface area and good dispersability in common solvents, graphenes are suitable platforms to anchor covalently units. The appended unit can introduce additional functionality to graphene. Although the field of covalently modified graphene is still starting compared to the development of other carbon nanoforms, there is already many examples describing the use of modified graphenes as recoverable photo-, electrocatalysts as well as in non-linear optics and to improve mechanical resistance and solubility of graphenes. In this Review, the state of the art of covalently modified graphenes for these applications is reviewed. After some general sections describing properties and characterization techniques of graphenes relevant to their use as supports and those general reactions and starting substrates to obtain the modified graphene conjugates, the main body of the review describes the preparation and properties of covalently modified graphene depending on their use as catalyst, photocatalyst, photoresponsive material, non-linear optics, electrocatalyst and other uses. The last section of the review summarizes the main achievements of the field and what should be according to our view the future developments.