As one of the most prevalent malignant tumours in women, breast cancer poses a serious threat to women's health worldwide. Its accurate pathological diagnosis not only relates to the choice of treatment plan for patients, but also directly affects the treatment effect and the quality of patients' survival. With the continuous progress of medical imaging technology, digital pathology images have gradually become the standard means of clinical diagnosis, which also brings the challenge of processing and analysing large amounts of data. Deep learning, especially convolutional neural networks (CNNs), has demonstrated significant advantages and potentials in automating the analysis of breast tumour pathology images, opening new avenues for improving the accuracy and efficiency of diagnosis. The aim of this review is to systematically explore the latest research advances and applications of deep learning, especially CNNs, in breast tumour pathology image classification, detection recognition and segmentation. This paper provides an in-depth analysis of the current technical challenges faced in this field, such as the problems of data scarcity, model interpretability, and model generalisation, and proposes possible solution strategies to these problems. Finally, this paper looks into future research directions, with special focus on how to fuse multimodal data, enhance model robustness and interpretability, with a view to providing useful references and insights for future research in the field of breast cancer pathology image analysis. Through this review, we hope to attract more researchers' attention, promote the research progress in this field, further promote the application of deep learning technology in clinical practice, and provide a more accurate decision basis for the early diagnosis of breast cancer as well as prognosis prediction.