Deep learning has introduced several learning-based methods to recognize breast tumours and presents high applicability in breast cancer diagnostics. It has presented itself as a practical installment in Computer-Aided Diagnostic (CAD) systems to further assist radiologists in diagnostics for different modalities. A deep learning network trained on images provided by hospitals or public databases can perform classification, detection, and segmentation of lesion types. Significant progress has been made in recognizing tumours on 2D images but recognizing 3D images remains a frontier so far. The interconnection of deep learning networks between different fields of study help propels discoveries for more efficient, accurate, and robust networks. In this review paper, the following topics will be explored: (i) theory and application of deep learning, (ii) progress of 2D, 2.5D, and 3D CNN approaches in breast tumour recognition from a performance metric perspective, and (iii) challenges faced in CNN approaches.