Artificial intelligence (AI) has invaded our daily lives, and in the last decade, there have been very promising applications of AI in the field of medicine, including medical imaging, in vitro diagnosis, intelligent rehabilitation, and prognosis. Breast cancer is one of the common malignant tumors in women and seriously threatens women's physical and mental health. Early screening for breast cancer via mammography, ultrasound and magnetic resonance imaging (MRI) can significantly improve the prognosis of patients. AI has shown excellent performance in image recognition tasks and has been widely studied in breast cancer screening. This paper introduces the background of AI and its application in breast medical imaging (mammography, ultrasound and MRI), such as in the identification, segmentation and classification of lesions; breast density assessment; and breast cancer risk assessment. In addition, we also discuss the challenges and future perspectives of the application of AI in medical imaging of the breast.