How to find attractive connections in public transportation for a planned trip is a challenging multi-criteria search problem which appears in several variants: as a pre-trip planning problem as well as an on-line problem. We give an overview of models and efficient algorithms for (optimally) solving timetable information problems in several realistic settings.

In daily operation, public transport always deviates from the planned schedule to a certain extent. Primary initial delays may cause a whole cascade of secondary delays of other trains, buses, planes, or the like over the entire network. This highly dynamic nature of the problem requires efficient update procedures. The inherent uncertainty about the development of delays asks for a stochastic view and requires methods for forecasting the delay development. We also survey recent results on robust pre-trip route planning. Finally, we close with some challenges for future research.