Disruptions of a railway system are responsible for longer travel times and much discomfort for the passengers. Since disruptions are inevitable, the railway system should be prepared to deal with them effectively. This paper explains that, in case of a disruption, rescheduling the timetable, the rolling stock circulation, and the crew duties is so complex that solving them manually is too time consuming in a time critical situation where every minute counts. Therefore, algorithmic support is badly needed. To that end, we describe models and algorithms for real-time rolling stock rescheduling and real-time crew rescheduling that are currently being developed and that are to be used as the kernel of decision support tools for disruption management. Furthermore, this paper argues that a stronger passenger orientation, facilitated by powerful algorithmic support, will allow to mitigate the adverse effects of the disruptions for the passengers. The latter will contribute to an increased service quality provided by the railway system. This will be instrumental in increasing the market share of the public transport system in the mobility market.