Abstract: LEO mega-constellation communication networks, characterized by their extensive coverage, low latency, and high bandwidth, are at the forefront of global communication network development. Furthermore, the exponential increase in satellite numbers presents unprecedented challenges to routing technology. This paper reviews the latest advancements and key challenges in LEO mega-constellation routing technology. Initially, it describes the network architecture of LEO mega-constellations. Subsequently, a detailed analysis was conducted on key technical issues including routing complexity, topology dynamics, load balancing, and latency. Moreover, it synthesizes current state of research on network topology management, load balancing strategies, latency optimization, and network robustness. Finally, the paper concludes by projecting future research trajectories in this technological field.