This review gives an overview of the current state of deep learning research in breast cancer imaging. Breast imaging plays a major role in detecting breast cancer at an earlier stage, as well as monitoring and evaluating breast cancer during treatment. The most commonly used modalities for breast imaging are digital mammography, digital breast tomosynthesis, ultrasound and magnetic resonance imaging. Nuclear medicine imaging techniques are used for detection and classification of axillary lymph nodes and distant staging in breast cancer imaging. All of these techniques are currently digitized, enabling the possibility to implement deep learning (DL), a subset of Artificial intelligence, in breast imaging. DL is nowadays embedded in a plethora of different tasks, such as lesion classification and segmentation, image reconstruction and generation, cancer risk prediction, and prediction and assessment of therapy response. Studies show similar and even better performances of DL algorithms compared to radiologists, although it is clear that large trials are needed, especially for ultrasound and magnetic resonance imaging, to exactly determine the added value of DL in breast cancer imaging. Studies on DL in nuclear medicine techniques are only sparsely available and further research is mandatory. Legal and ethical issues need to be considered before the role of DL can expand to its full potential in clinical breast care practice.