Intelligent escape is an interdisciplinary field that employs artificial intelligence (AI) techniques to enable robots with the capacity to intelligently react to potential dangers in dynamic, intricate, and unpredictable scenarios. As the emphasis on safety becomes increasingly paramount and advancements in robotic technologies continue to advance, a wide range of intelligent escape methodologies has been developed in recent years. This paper presents a comprehensive survey of state-of-the-art research work on intelligent escape of robotic systems. Four main methods of intelligent escape are reviewed, including planning-based methodologies, partitioning-based methodologies, learning-based methodologies, and bio-inspired methodologies. The strengths and limitations of existing methods are summarized. In addition, potential applications of intelligent escape are discussed in various domains, such as search and rescue, evacuation, military security, and healthcare. In an effort to develop new approaches to intelligent escape, this survey identifies current research challenges and provides insights into future research trends in intelligent escape.