The review paper provides the perceptible description of Breast Cancer (BC) and its classification and various classification strategies associated with BC. It discusses the related studies pertaining to the analysis and classification of BC through histopathological images and investigates the crucial advancements in the BC classification procedures. Furthermore, it provides the analysis of breast histopathological images using traditional Artificial Neural Networks (ANNs). The paper discusses the distinct Deep Learning (DL) methods involved in enhancing the performance of BC classification. By discussing all major studies this review assists researchers in better classification and analysis of BC thereby providing a concise perspective of existing issues, solutions and further developments.