Breast cancer has reached the highest incidence rate worldwide among all malignancies since 2020. Breast imaging plays a significant role in early diagnosis and intervention to improve the outcome of breast cancer patients. In the past decade, deep learning has shown remarkable progress in breast cancer imaging analysis, holding great promise in interpreting the rich information and complex context of breast imaging modalities. Considering the rapid improvement in deep learning technology and the increasing severity of breast cancer, it is critical to summarize past progress and identify future challenges to be addressed. This paper provides an extensive review of deep learning-based breast cancer imaging research, covering studies on mammograms, ultrasound, magnetic resonance imaging, and digital pathology images over the past decade. The major deep learning methods and applications on imaging-based screening, diagnosis, treatment response prediction, and prognosis are elaborated and discussed. Drawn from the findings of this survey, we present a comprehensive discussion of the challenges and potential avenues for future research in deep learning-based breast cancer imaging.