Model-based approaches for image reconstruction, analysis and interpretation have made significant progress over the last decades. Many of these approaches are based on either mathematical, physical or biological models. A challenge for these approaches is the modelling of the underlying processes (e.g. the physics of image acquisition or the patho-physiology of a disease) with appropriate levels of detail and realism. With the availability of large amounts of imaging data and machine learning (in particular deep learning) techniques, data-driven approaches have become more widespread for use in different tasks in reconstruction, analysis and interpretation. These approaches learn statistical models directly from labelled or unlabeled image data and have been shown to be very powerful for extracting clinically useful information from medical imaging. While these data-driven approaches often outperform traditional model-based approaches, their clinical deployment often poses challenges in terms of robustness, generalization ability and interpretability. In this article, we discuss what developments have motivated the shift from model-based approaches towards data-driven strategies and what potential problems are associated with the move towards purely data-driven approaches, in particular deep learning. We also discuss some of the open challenges for data-driven approaches, e.g. generalization to new unseen data (e.g. transfer learning), robustness to adversarial attacks and interpretability. Finally, we conclude with a discussion on how these approaches may lead to the development of more closely coupled imaging pipelines that are optimized in an end-to-end fashion.All steps of the medical imaging pipeline typically make extensive use of models. In this paper we define the term model in a very general fashion, in the sense that it provides a transformation of input (data) into the desired output. For example, in image reconstruction the model helps to transform the acquired sensor data into an image, in image registration the model is used to relate two images (inputs) via a transformation (output), and in image segmentation the model is used to transform an image in which each pixel corresponds to an intensity value, into an semantic segmentation where each pixel has a label corresponding to an organ, anatomical structure or pathology. In diagnosis, the model helps to map image derived features and biomarkers