Artificial Intelligence (AI), in particular Generative Artificial Intelligence (GenAI), is a quickly developing field capable of revolutionizing educational digital escape rooms. Traditionally reliant on static content, these immersive environments have faced limitations in adaptability, replayability, and personalization. However, recent advancements in AI and GenAI enable dynamic puzzle generation, adaptive storytelling, and AI-driven non-player characters (NPCs) with agentic AI, allowing for highly responsive and personalized experiences. This paper reviews the state-of-the-art in integrating AI (with the focus on GenAI) into educational digital escape rooms, integrating interdisciplinary insights from cognitive science, game design, and machine learning, and showing how AI can improve engagement, scalability, and content diversity, but also indicates challenges related to ethical AI use, bias in algorithmic decision-making, and the need for robust evaluation frameworks to assess player satisfaction and learning outcomes.