The routine operation of modern healthcare systems produces a wealth of data in electronic health records, administrative databases, clinical registries, and other clinical systems. It is widely acknowledged that there is great potential for utilising these routine data for health research to derive new knowledge about health, disease, and treatments. However, the reuse of routine healthcare data for research is not beyond debate. In this paper, we discuss three issues that have stirred considerable controversy among health data scientists. First, we discuss van der Lei's 1st Law of Medical Informatics, which states that data shall be used only for the purpose for which they were collected. Then, we discuss to which extent routine data sources and innovations in analytical methods alleviate the need to conduct randomised clinical trials. Finally, we address questions of governance, privacy, and trust when routine health data are made available for research. While we don't think that there is a definite "right answer" for any of these issues, we argue that data scientists should be aware of the arguments for different viewpoints, respect their validity, and contribute constructively to the debate. The three controversies discussed in this paper relate to core challenges for research with health data and define an essential research agenda for the health data science community.