Understanding the complementary roles of surface roughness and energy in natural super-non-wetting surfaces has greatly promoted the development of biomimetic superhydrophobic surfaces that repel water at a much greater rate than oils. These surfaces that are highly repellent to low-surface-tension oils and organic liquids, termed superoleophobic surfaces, are poorly understood. Inspired by springtails (collembolan), a third factor, re-entrant surface curvature, has been introduced to the design and fabrication system of superoleophobic surfaces in conjunction with two other factors of surface chemical composition and roughness. Over the past decade, superoleophobic surfaces have attracted tremendous attention with respect to their design, fabrication and applications due to their extraordinary properties. This review focuses on these aspects and thus summarizes recent research progress in superoleophobic surfaces. Starting from the origin, features of natural oil-resistant creatures have been introduced, and fundamental theories for surface design have been discussed. Calculations suggest that creation of these surfaces requires specific re-entrant structures and fluoride modifiers. Based on this principle, various fabrication methods, from top-down to bottom-up approaches, have been used, and some derivative structures with desirable properties have been produced. A precise and detailed classification has been provided in this review that includes representative methods and structures as well as functions (i.e., transparence and self-healing). Significantly, superoleophobic materials have many valuable applications, including oil pollution resistance, oil transportation, and synthesis of mesoporous supraparticles. However, their complicated manufacturing techniques, poor physical–chemical properties and environmentally unfriendly surface chemicals jointly impede their real-life applications. Therefore, it is highly necessary to optimize the craft and performance of theses surfaces for industrial operation and practical applications. To this end, some challenges and perspectives will be provided regarding the future research and development of superoleophobic surfaces.