Liquid-repellent surfaces, such as superhydrophobic surfaces, superoleophobic surfaces, and slippery liquid-infused surfaces, have drawn keen research interest from the communities engaged in chemical synthesis, interfacial chemistry, surface engineering, bionic manufacturing and micro-nano machining. This is due to their great potential applications in liquid-proofing, self-cleaning, chemical resistance, anti-icing, water/oil remediation, biomedicine, etc. However, poor robustness and durability that notably hinders the real-world applications of such surfaces remains their Achilles heel. The past few years have witnessed rapidly increasing publications that address the robustness and durability of liquid-repellent surfaces, and many breakthroughs have been achieved. This review provides an overview of the recent progress made towards robust and durable liquid-repellent surfaces. First, we discuss the wetting of solid surface and its generally-adopted characterisation methods, and introduce typical liquid-repellent surfaces. Second, we focus on various evaluation methods of the robustness and durability of liquid-repellent surfaces. Third, the recent advances in design and fabrication of robust and durable liquid-repellent surfaces are reviewed in detail. Fourth, we present the applications where these surfaces have been employed in fields like chemistry, engineering, biology and in daily life. Finally, we discuss the possible research perspectives in robust and durable liquid-repellent surfaces. By presenting such state-of-the-art of this significant and fast-developing area, we believe that this review will inspire multidisciplinary scientific communities and industrial circles to develop novel liquid-repellent surfaces that can meet the requirements of various real-world applications.