Surfaces that display contact angles 41501 along with low contact angle hysteresis with essentially all high and low surface tension liquids, including water, oils and alcohols, are known as superomniphobic surfaces. Such surfaces have a range of commercial applications, including self-cleaning, non-fouling, stain-free clothing, drag reduction, corrosion prevention and separation of liquids. Such surfaces have thus generated immense academic and industrial interest in recent years. In this review, we discuss the systematic design of superomniphobic surfaces. In particular, we discuss the significance of surface energy, roughness and the critical role of re-entrant texture in obtaining the so-called Cassie-Baxter state with low surface tension liquids. We also discuss how hierarchical scales of texture can yield high contact angles and decrease the contact angle hysteresis of superomniphobic surfaces by reducing the solid-liquid contact area. On the basis of this understanding, we discuss dimensionless design parameters that allow for the systematic design of superomniphobic surfaces. We also review the current literature on superomniphobic surfaces, paying particular attention to surfaces that demonstrate good mechanical, chemical and radiation durability-traits that are essential for any commercial application of superomniphobic surfaces. Finally, we conclude by identifying the unresolved challenges in the fabrication of durable superomniphobic surfaces and highlight the future needs in the field.