Breast cancer in women is the second most common cancer worldwide. Early detection of breast cancer can reduce the risk of human life. Non-invasive techniques such as mammograms and ultrasound imaging are popularly used to detect the tumour. However, histopathological analysis is necessary to determine the malignancy of the tumour as it analyses the image at the cellular level. Manual analysis of these slides is time consuming, tedious, subjective and are susceptible to human errors. Also, at times the interpretation of these images are inconsistent between laboratories. Hence, a Computer-Aided Diagnostic system that can act as a decision support system is need of the hour. Moreover, recent developments in computational power and memory capacity led to the application of computer tools and medical image processing techniques to process and analyze breast cancer histopathological images. This review paper summarizes various traditional and deep learning based methods developed to analyze breast cancer histopathological images. Initially, the characteristics of breast cancer histopathological images are discussed. A detailed discussion on the various potential regions of interest is presented which is crucial for the development of Computer-Aided Diagnostic systems. We summarize the recent trends and choices made during the selection of medical image processing techniques. Finally, a detailed discussion on the various challenges involved in the analysis of BCHI is presented along with the future scope.