Soft robots, compared to rigid robots, possess inherent advantages, including higher degrees of freedom, compliance, and enhanced safety, which have contributed to their increasing application across various fields. Among these benefits, adaptability is particularly noteworthy. In this paper, adaptability in soft robots is categorized into external and internal adaptability. External adaptability refers to the robot's ability to adjust, either passively or actively, to variations in environments, object properties, geometries, and task dynamics. Internal adaptability refers to the robot's ability to cope with internal variations, such as manufacturing tolerances or material aging, and to generalize control strategies across different robots. As the field of soft robotics continues to evolve, the significance of adaptability has become increasingly pronounced. In this review, we summarize various approaches to enhancing the adaptability of soft robots, including design, sensing, and control strategies. Additionally, we assess the impact of adaptability on applications such as surgery, wearable devices, locomotion, and manipulation. We also discuss the limitations of soft robotics adaptability and prospective directions for future research. By analyzing adaptability through the lenses of implementation, application, and challenges, this paper aims to provide a comprehensive understanding of this essential characteristic in soft robotics and its implications for diverse applications.