The study presented in the article is focused on use of graphene obtained by novel microwave-enhanced chemical vapor deposition (MECVD) method as a construction material for 3D porous structures—aerogels and sponges. MECVD graphene nanoplatelets-based aerogels were obtained by mixing MECVD graphene nanoplatelets and chitosan, dissolved in 3% acetic acid followed by its freeze drying and carbonization at 800° in inert medium. Surface morphology of aerogels was characterized by SEM. MECVD graphene nanoplatelets-based aerogels are characterized by a porous structure; they are superhydrophobic and possess high sorption capacity with regard to organic liquids of different densities. Polyurethane sponges coated with MECVD graphene can serve as an alternative to aerogels. The process of their obtaining is cheaper and less complicated. They were obtained by facile “dip-coating” method, modifying its surface to increase its hydrophobicity. The resulting sponges are superhydrophobic and superoleophilic, and demonstrate high rate of sorption of organic liquids and can be easily regenerated by squeezing. In addition, they can be used as a separating material in conjunction with vacuum system for continuous and selective collection of organic liquids from the surface of water.