Management of crowd information in public transportation (PT) systems is crucial, both to foster sustainable mobility, by increasing the user's comfort and satisfaction during normal operation, as well as to cope with emergency situations, such as pandemic crises, as recently experienced with COVID-19 limitations. This paper presents a taxonomy and review of sensing technologies based on Internet of Things (IoT) for real-time crowd analysis, which can be adopted in the different segments of the PT system (buses/trams/trains, railway/metro stations, and bus/tram stops). To discuss such technologies in a clear systematic perspective, we introduce a reference architecture for crowd management, which employs modern information and communication technologies (ICT) in order to: (i) monitor and predict crowding events; (ii) implement crowd-aware policies for real-time and adaptive operation control in intelligent transportation systems (ITSs); (iii) inform in real-time the users of the crowding status of the PT system, by means of electronic displays installed inside vehicles or at bus/tram stops/stations, and/or by mobile transport applications. It is envisioned that the innovative crowd management functionalities enabled by ICT/IoT sensing technologies can be incrementally implemented as an add-on to state-of-the-art ITS platforms, which are already in use by major PT companies operating in urban areas. Moreover, it is argued that, in this new framework, additional services can be delivered to the passengers, such as, e.g., on-line ticketing, vehicle access control and reservation in severely crowded situations, and evolved crowd-aware route planning.