Over the past decade, medical imaging research has grown significantly in image processing and computer vision, particularly in detecting, classifying, and segmenting breast cancer. Advancements in pattern recognition and Deep learning (DL) methodologies have significantly impacted this field. In light of the swift advancements in deep learning technology and the escalating seriousness of breast cancer, it is imperative to synthesize previous achievements and pinpoint forthcoming obstacles that require attention. Thus, this paper extensively reviews the classification of histopathological images for breast cancer detection using machine learning and deep learning techniques. The article emphasizes the publicly accessible datasets of histopathological images for classifying breast cancer. This article examines and outlines recent research on histopathology imaging for breast cancer screening and explores potential future developments. Upon reviewing the literature, it was discovered that only a limited number of studies utilize image processing and machine learning approaches. Most research in the past five years has utilized deep learning techniques.