Network-based systems are at the core of our everyday life. Whether it is electronic networking, electricity grids or transportation, users expect the networks to function properly and provide a feeling of safety and security. However, there may be disturbances. In this paper, we consider disturbances in the context of public transportation. The focus in this respect is on public transport planning and operations. To classify and cope with disturbances, one can find many ideas, including robustness, resilience, vulnerability, disruption mitigation or delay management. We survey related streams of literature and put them into perspective. As a major insight we show that different strands of literature exist that may benefit from becoming better connected and intertwined. Together with recent advances in information technology and solution methods, more integrated problem settings incorporating robustness and disturbances can play a major role in future planning and operations.