Abstract: Frequent oil spill accidents and the massive discharge of industrial oily sewage have destroyed the ecological balance and threatened marine life. Graphene (G) and graphene oxide (GO) have emerged as important materials in the field of oil/water separation because of their remarkable physicochemical properties including high specific surface area, low density, high porosity and tailorable surface functionality. To take full advantage of G and GO, their incorporation with polymers to build functional G/polymer and GO/polymer composites has recently gained increasing popularity because of their improved oil clean-up capability, outstanding mechanical performance, relatively low cost and adjustable surface chemical composition. Tremendous efforts have contributed to the development of G/polymer and GO/polymer composite oil clean-up sorbents and filtration membranes in 3D structural forms such as aerogels, foams, sponges and membranes. In this review, a comprehensive picture from the basic theory of the surface wettability to the recent advances in G/polymer and GO/polymer composite oil clean-up sorbents and filtration membranes are highlighted. The strategies for oil recovery and regeneration of the sorbents are also summarized. Current challenges and future research directions in this topic are provided, aimed at providing new perspectives for in-depth exploration in this field.