Nature provides a range of functional surfaces, for example, water-repellent or superhydrophobic surfaces, most common among them the lotus leaf. While water-repellency is widespread in nature, oil-repellency is typically limited to surfaces submerged in water, such as fish scales. To achieve oleophobicity in air, inspiration must be taken from natural structures and chemistries that are not readily available in nature need to be introduced. Researchers usually turn to fluorinated materials to provide the low surface energy that, when combined with bioinspired surface topography, is the key to unlocking oil-repellency. This review presents the state-of-the-art in the fabrication of superoleophobic surfaces.