Surfaces that display liquid contact angles greater than 150° along with low contact angle hysteresis for liquids with both high and low surface tension values are known as superomniphobic surfaces. Such surfaces are of interest for a diverse array of applications, including self-cleaning surfaces, nonfouling surfaces, stain-free clothing, spill-resistant protective wear, drag reduction, and fingerprint-resistant surfaces. Recently, significant advances have been made in understanding the criteria required to design superomniphobic surfaces. In this article, we discuss the roles of surface energy, roughness, re-entrant texture, and hierarchical structure in fabricating superomniphobic surfaces. We also provide a review of different superomniphobic surfaces reported recently in the literature and emphasize the need for mechanical, chemical, and radiation durability of superomniphobic surfaces for practical applications. Finally, we conclude with a discussion of the unresolved challenges in developing durable superomniphobic surfaces that define the scope for further improvements in the field.