Over the last decade, research in medical imaging has made significant progress in addressing challenging tasks such as image registration and image segmentation. In particular, the use of model-based approaches has been key in numerous, successful advances in methodology. The advantage of model-based approaches is that they allow the incorporation of prior knowledge acting as a regularisation that favours plausible solutions over implausible ones. More recently, medical imaging has moved away from hand-crafted, and often explicitly designed models towards data-driven, implicit models that are constructed using machine learning techniques. This has led to major improvements in all stages of the medical imaging pipeline, from acquisition and reconstruction to analysis and interpretation. As more and more imaging data is becoming available, e.g., from large population studies, this trend is likely to continue and accelerate. At the same time new developments in machine learning, e.g., deep learning, as well as significant improvements in computing power, e.g., parallelisation on graphics hardware, offer new potential for data-driven, semantic and intelligent medical imaging. This article outlines the work of the BioMedIA group in this area and highlights some of the challenges and opportunities for future work.