• MAX series materials exhibit a unique combination of metallic and ceramic properties due to their laminated crystal structure, enabling diverse functional applications.
• The review systematically covers the research timeline, structural diversity, synthesis routes, and prediction methods (including machine learning) for MAX materials.
• Over 383 different MAX phases have been reported, with novel compositions predicted via theoretical simulation and machine learning.
• Key challenges for future development include accelerating the transition of MAX materials into new quality productive forces for advanced technological applications.