The separation of oil from oily water is an important pursuit because of increasing worldwide oil pollution. Separation by the use of materials with selective oil/water absorption is a relatively recent area of development, yet highly promising. Owing to their selective superantiwetting/superwetting properties towards water and oil, superhydrophobic/superoleophilic surfaces and underwater superoleophobic surfaces have been developed for the separation of oil/water-free mixtures and emulsions. In this Review, after a short introduction to oil/water separation, we describe the principles of materials with selective oil/water absorption and outline recent advances in oil/water separation with superwetting/superantiwetting materials, including their design, their fabrication, and models of experimental setups. Finally, we discuss the current state of this new field and point out the remaining problems and future challenges.