Railway operations are highly susceptible to delays and disruptions caused by various factors, such as technical issues, operational inefficiencies, and unforeseen events. To counter these delays and ensure efficient railway operations during real-time management, several rescheduling approaches can be implemented. Among these approaches, passenger-oriented rescheduling considers train rescheduling while taking passenger data into account, as opposed to operation-oriented rescheduling. This paper provides an overview of the former group of approaches. Particular focus is put on different ways passenger data is exploited to optimize rescheduling and on the measures the approaches can decide on. The rescheduling measures typically considered vary from decisions on maintaining transfers, canceling trains, adding emergency trains, changing routes and orders of trains, skipping or adding stops at stations, short turning trains, applying speed control and modifying rolling stock compositions. In this regard, the paper presents a comprehensive analysis of real-time rescheduling approaches adopted in both conventional and urban rail transits, and points out possible directions for further research in the field.