Graphene, the 2D form of carbon based material existing as a single layer of atoms arranged in a honeycomb lattice, has set the science and technology sectors alight with interest in the last decade in view of its astounding electrical and thermal properties, combined with its mechanical stiffness, strength and elasticity. Two distinct strategies have been undertaken for graphene production, i.e. the bottom-up and the top-down. The former relies on the generation of graphene from suitably designed molecular building blocks undergoing chemical reaction to form covalently linked 2D networks. The latter occurs via exfoliation of graphite into graphene. Bottom-up techniques, based on the organic syntheses starting from small molecular modules, when performed in liquid media, are both size limited, because macromolecules become more and more insoluble with increasing size, and suffer from the occurrence of side reactions with increasing molecular weight. Because of these reasons such a synthesis has been performed more and more on a solid (ideally catalytically active) surface. Substrate-based growth of single layers can be done also by chemical vapor deposition (CVD) or via reduction of silicon carbide, which unfortunately relies on the ability to follow a narrow thermodynamic path. Top-down approaches can be accomplished under different environmental conditions. Alongside the mechanical cleavage based on the scotch tape approach, liquid-phase exfoliation (LPE) methods are becoming more and more interesting because they are extremely versatile, potentially up-scalable, and can be used to deposit graphene in a variety of environments and on different substrates not available using mechanical cleavage or growth methods. Interestingly, LPE can be applied to produce different layered systems exhibiting different compositions such as BN, MoS2, WS2, NbSe2, and TaS2, thereby enabling the tuning of numerous physico-chemical properties of the material. Furthermore, LPE can be employed to produce graphene-based composites or films, which are key components for many applications, such as thin-film transistors, conductive transparent electrodes for indium tin oxide replacement, e.g. in light-emitting diodes, or photovoltaics. In this review, we highlight the recent progress that has led to successful production of high quality graphene by means of LPE of graphite. In particular, we discuss the mechanisms of exfoliation and methods that are employed for graphene characterization. We then describe a variety of successful liquid-phase exfoliation methods by categorizing them into two major classes, i.e. surfactant-free and surfactant-assisted LPE. Furthermore, exfoliation in aqueous and organic solutions is presented and discussed separately.