The demand for rail transport is expected to increase due to growing mobility needs and shifts in transport policies. This growth will lead to a higher capacity utilization of existing networks, making disturbances more frequent. To minimize their impact, dispatchers engage in real-time traffic management by adjusting the timetable to resolve the arising conflicts. Given the limited time to identify high-quality solutions, developing computer-based optimization methods to support dispatchers can significantly enhance rail transport efficiency. However, this is a challenging task with high computational complexity particularly in large and dense railway networks. Quantum computing offers a possible research direction, as it may offer advantages over classical computing due to its unique properties. This paper introduces the fundamentals of quantum computing and explores its challenges and opportunities for real-time railway traffic management. For this purpose, the paper reviews existing approaches that use quantum computing in railway operations and related fields, and highlights open challenges. Finally, several further research directions are identified, ranging from detailed benchmarking to new algorithm development.