Since its emergence in 2004, graphene has attracted enormous attention because of its unique and fantastic properties, which signals the birth of two-dimensional (2D) nanomaterials. The strictly atomic-layered 2D structure endows graphene with unconventional optical, electronic, magnetic, and mechanical properties. Owing to these extraordinary features, graphene has exhibited great potential in various fields, such as biology, medicine, chemistry, physics, and the environment. Notably, when graphene is used in these fields, it is always functionalized to facilitate its manipulation or meet the different area demands. After functionalization, the properties of graphene, such as its composition, size, shape, and structure, are modified, leading to changes in its electronic structure, surface chemistry, solubility, and mechanical and chemical properties. Functionalization of graphene can be achieved through various approaches, including chemical oxidation, doping, covalent and non-covalent modification, and hybridization with other materials, yielding various products (i.e., graphene oxide, nano graphene, graphene nanoribbons (GNRs), graphene nanomeshes, and graphene-polymer hybrids). However, these resulting products have not been systematically classified or strictly defined until now; although they have been classified as covalent and non-covalent functionalized graphene, graphene-based polymer composites, and graphene-based composites. Systematic classification and exact definition will benefit research on functionalizing graphene. In this review, based on research on functionalization of graphene, we propose a systematic classification of the products from graphene functionalization, their corresponding definitions, and preparation strategies, which are illustrated by representative examples. All the products from graphene functionalization are defined as functionalized graphene materials, which fall into two categories: functionalized graphene and functionalized graphene composite. Functionalized graphene is the product of modifying graphene by tuning its composition, framework, dimension, and morphology, and functionalized graphene composites are hybrids of graphene (or functionalized graphene) with other materials, including small molecules, polymers, metals, inorganic compounds, and carbon nanotubes (CNTs). Functionalized graphene materials are prepared through two strategies: "top-down" and "bottom-up," each of which has its advantages and shortcomings and includes many corresponding preparation methods. The selection of preparation strategies depends on the application requirements, as different applications require different types of graphene. Both strategies are elucidated with detailed examples through an extensive analysis of the literature. Finally, the major challenges and perspectives of functionalized graphene materials are discussed. This review presents the proposed systematic classification and exact definition of functionalized graphene materials, which can enhance their development. It is bel...