Although graphene's physical structure is a single atom thick, two-dimensional, hexagonal crystal of sp(2) bonded carbon, this simple description belies the myriad interesting and complex physical properties attributed to this fascinating material. Because of its unusual electronic structure and superlative properties, graphene serves as a leading candidate for many next generation technologies including high frequency electronics, broadband photodetectors, biological and gas sensors, and transparent conductive coatings. Despite this promise, researchers could apply graphene more routinely in real-world technologies if they could chemically adjust graphene's electronic properties. For example, the covalent modification of graphene to create a band gap comparable to silicon (∼1 eV) would enable its use in digital electronics, and larger band gaps would provide new opportunities for graphene-based photonics. Toward this end, researchers have focused considerable effort on the chemical functionalization of graphene. Due to its high thermodynamic stability and chemical inertness, new methods and techniques are required to create covalent bonds without promoting undesirable side reactions or irreversible damage to the underlying carbon lattice. In this Account, we review and discuss recent theoretical and experimental work studying covalent modifications to graphene using gas phase atomic radicals. Atomic radicals have sufficient energy to overcome the kinetic and thermodynamic barriers associated with covalent reactions on the basal plane of graphene but lack the energy required to break the C-C sigma bonds that would destroy the carbon lattice. Furthermore, because they are atomic species, radicals substantially reduce the likelihood of unwanted side reactions that confound other covalent chemistries. Overall, these methods based on atomic radicals show promise for the homogeneous functionalization of graphene and the production of new classes of two-dimensional materials with fundamentally different electronic and physical properties. Specifically, we focus on recent studies of the addition of atomic hydrogen, fluorine, and oxygen to the basal plane of graphene. In each of these reactions, a high energy, activating step initiates the process, breaking the local π structure and distorting the surrounding lattice. Scanning tunneling microscopy experiments reveal that substrate mediated interactions often dominate when the initial binding event occurs. We then compare these substrate effects with the results of theoretical studies that typically assume a vacuum environment. As the surface coverage increases, clusters often form around the initial distortion, and the stoichiometric composition of the saturated end product depends strongly on both the substrate and reactant species. In addition to these chemical and structural observations, we review how covalent modification can extend the range of physical properties that are achievable in two-dimensional materials.