The planning and implementation of public transport involves many data sources. These data sources in turn generate a high volume of data, in a wide variety of formats and data rates. This phenomenon is reinforced by the ongoing digitization of public transport; new data sources have continuously emerged in public transport in recent years and decades. This results in a great potential for the application and utilization of data science methods in public transport. Using big data methods and sources can, or in some cases already does, contribute to a better understanding and the further optimization of public transport networks, public transport service and public transport in general. This paper classifies data sources in the field of public transport and examines systematically for which use cases the data are used or can be used. These steps contribute by structuring ongoing discussions about the application of data science in the public transport domain and illustrate the potential of the application of data science for public transport. We present several use cases in which we applied data science methods, such as machine learning and visualization to public transport data. Several of these projects use data from automated passenger information systems, a data source that has not been widely studied to date. We report our findings for these use cases and discuss the lessons learned, to inform future research on these use cases and discuss their potential. This paper concludes with a summary of the typical problems that occur when dealing with big public transport data and a discussion of solutions for these problems. This discussion identifies future work and topics worth investigating for public transport companies as well as for researchers. Working on these topics will, in our opinion, support the improvement of public transport towards the efficiency and attractiveness that is needed for public transport to play its essential role in future sustainable mobility. The application of these methods in public transport requires the collaboration of domain experts with researchers and data scientists, calling for a mutual understanding. This paper also contributes to this understanding by providing an overview of the methods that are already used, potential new use cases, data sources, challenges and possible solutions.