Selective filtration of gas, water, and liquid or gaseous oil is essential to prevent possible environmental pollution and machine/facility malfunction in oil-based industries. Novel materials and structures able to selectively and efficiently filter liquid and vapor in various types of solutions are therefore in continuous demand. Here, we investigate selective gas-water-oil filtration using three-dimensional graphene structures. The proposed approach is based on the adjustable wettability of three-dimensional graphene foams. Three such structures are developed in this study; the first allows gas, oil, and water to pass, the second blocks water only, and the third is exclusively permeable to gas. In addition, the ability of three-dimensional graphene structures with a self-assembled monolayer to selectively filter oil is demonstrated. This methodology has numerous potential practical applications as gas, water, and/or oil filtration is an essential component of many industries.