Soft robotics has emerged as a transformative technology in Search and Rescue (SAR) operations, addressing challenges in navigating complex, hazardous environments that often limit traditional rigid robots. This paper critically examines advancements in soft robotic technologies tailored for SAR applications, focusing on their unique capabilities in adaptability, safety, and efficiency. By leveraging bio-inspired designs, flexible materials, and advanced locomotion mechanisms, such as crawling, rolling, and shape morphing, soft robots demonstrate exceptional potential in disaster scenarios. However, significant barriers persist, including material durability, power inefficiency, sensor integration, and control complexity. This comprehensive review highlights the current state of soft robotics in SAR, discusses simulation methodologies and hardware validations, and introduces performance metrics essential for their evaluation. By bridging the gap between theoretical advancements and practical deployment, this study underscores the potential of soft robotic systems to revolutionize SAR missions and advocates for continued interdisciplinary innovation to overcome existing limitations.