Breast cancer is one of the largest causes of women's death in the world today. Advance engineering of natural image classification techniques and Artificial Intelligence methods has largely been used for the breast-image classification task. The involvement of digital image classification allows the doctor and the physicians a second opinion, and it saves the doctors' and physicians' time. Despite the various publications on breast image classification, very few review papers are available which provide a detailed description of breast cancer image classification techniques, feature extraction and selection procedures, classification measuring parameterizations, and image classification findings. We have put a special emphasis on the Convolutional Neural Network (CNN) method for breast image classification. Along with the CNN method we have also described the involvement of the conventional Neural Network (NN), Logic Based classifiers such as the Random Forest (RF) algorithm, Support Vector Machines (SVM), Bayesian methods, and a few of the semisupervised and unsupervised methods which have been used for breast image classification.