Breast cancer is a common malignant tumour and studies have shown that early and accurate detection is crucial for patients. With the maturity of medical imaging and deep learning development, significant progress has been made in breast cancer classification, which greatly improves the accuracy and efficiency of classification. This review focuses on deep learning, migration learning, GAN, and lifelong learning to elaborate and summarise the important roles arising from breast cancer detection. This review also examines the dataset and labeling issues required for breast cancer classification. In conclusion, at the end of the article, we look at future directions for breast cancer classification research, including cross-migration learning, multimodal data fusion, model interpretability, and lifelong learning, and also explore how to provide personalized treatment plans for patients.