Imaging and cardiology are the healthcare domains which have seen the greatest number of FDA approvals for novel data-driven technologies, such as artificial intelligence, in recent years. The increasing use of such data-driven technologies in healthcare is presenting a series of important challenges to healthcare practitioners, policymakers, and patients. In this paper, we review ten ethical, social, and political challenges raised by these technologies. These range from relatively pragmatic concerns about data acquisition to potentially more abstract issues around how these technologies will impact the relationships between practitioners and their patients, and between healthcare providers themselves. We describe what is being done in the United Kingdom to identify the principles that should guide AI development for health applications, as well as more recent efforts to convert adherence to these principles into more practical policy. We also consider the approaches being taken by healthcare organizations and regulators in the European Union, the United States, and other countries. Finally, we discuss ways by which researchers and frontline clinicians, in cardiac imaging and more broadly, can ensure that these technologies are acceptable to their patients.