Superoleophobicity is a phenomenon where the contact angles of various oil droplets with low surface tension on a solid surface are larger than 150°. In the past few years, there has been much growing interest in the design and application of superoleophobic surfaces. Such surfaces have great significance for both fundamental research and a variety of practical applications, including oil-repellent coatings, self-cleaning, oil/water separation, oil droplet manipulation, chemical shielding, anti-blocking, designing liquid microlens, oil capture, bioadhesion, guiding oil movement and floating on oil. Herein, we systematically summarize the recent developments of superoleophobic surfaces. This review focuses on the design, fabrication, characteristics, functions, and important applications of various superoleophobic surfaces. Although many significant advances have been achieved, superoleophobic surfaces are still in their "toddler stage" of development. The current challenges and future prospects of this fast-growing field of superoleophobicity are discussed.