Machine learning (ML) algorithms have made a tremendous impact in the field of medical imaging. While medical imaging datasets have been growing in size, a challenge for supervised ML algorithms that is frequently mentioned is the lack of annotated data. As a result, various methods that can learn with less/other types of supervision, have been proposed. We give an overview of semi-supervised, multiple instance, and transfer learning in medical imaging, both in diagnosis or segmentation tasks. We also discuss connections between these learning scenarios, and opportunities for future research.