Graphene, graphene oxide (GO), and their composites have been prominently utilized for wastewater purification because of their adsorption, oxidation, and catalytic properties. Graphene and GO and its composites naturally have significant pore volume, high conductivity, rich surface chemistry, and an exceptionally large aspect ratio which make it favorable for adsorption and catalysis of organic pollutants from wastewater. The sheet-like, resonating, polyaromatic pi-system of graphene subsidiaries play a significant role in pi-pi interactions, hydrogen bonding, and/or electrostatic interactions with organic pollutants that include dyes, pharmaceutical waste, and agricultural and industrial effluents whose base structure consists of notably reactive unsaturated aromatic rings and oxygen-rich functional groups. The adsorption capacities of pollutants have been widely researched and catalogued by considering the adsorption isotherm (Langmuir, Freundlich, Temkin, DR model) they fit, the kinetic models (pseudo-first-order, pseudo-second-order, Elovich, and intraparticle diffusion) they follow, the parameters that affect the process (pH, temperature, etc.) and the reusability of the adsorbent. The photocatalytic efficiency has been anthologized with the viewpoint of the radicals being involved in photocatalysis and the light source used for the process. This review focuses on adsorption, advanced oxidation, and catalysis of various emerging organic pollutants using graphene subsidiaries, graphene-based composites, and hybrids; proves their efficacy as multifunctional materials for the expulsion of toxic aqueous phase pollutants; and presents new prospects for designing advanced water treatment strategies.