External and internal factors can cause disturbances or disruptions in daily train operations, leading to deviations from official timetables and passenger delays. As a result, efficient train timetable rescheduling (TTR) methods are necessary to restore disrupted train services. Although TTR has been a popular research topic in recent years, the uncertain characteristics of railways have not been sufficiently addressed. This review first identifies the primary uncertainties of TTR and examines their impacts on both TTR and passenger routing during disturbances or disruptions. It finds that only a few uncertainties have been investigated, and the existing solution methods do not adequately meet practical requirements, such as considering the dynamic nature of disturbances or disruptions, which is crucial for real-world applications. Therefore, the review highlights problems associated with TTR uncertainties that need urgent attention and suggests promising methodologies that could effectively address these issues as future research directions. This review aims to help practitioners develop improved automatic train-dispatching systems with better train-rescheduling performance under disturbances or disruptions compared to current systems.