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Breast cancer is a common and fatal disease among women worldwide. Therefore, the early and precise diagnosis of breast cancer plays a pivotal role to improve the prognosis of patients with this disease. Several studies have developed automated techniques using different medical imaging modalities to predict breast cancer development. However, few review studies are available to recapitulate the existing literature on breast cancer classification. These studies provide an overview of the classification, segmentation, or grading of many cancer types, including breast cancer, by using traditional machine learning approaches through hand-engineered features. This review focuses on breast cancer classification by using medical imaging multimodalities through state-of-the-art artificial deep neural network approaches. It is anticipated to maximize the procedural decision analysis in five aspects, such as types of imaging modalities, datasets and their categories, pre-processing techniques, types of deep neural network, and performance metrics used for breast cancer classification. Forty-nine journal and conference publications from eight academic repositories were methodically selected and carefully reviewed from the perspective of the five aforementioned aspects. In addition, this study provided quantitative, qualitative, and critical analyses of the five aspects. This review showed that mammograms and histopathologic images were mostly used to classify breast cancer. Moreover, about 55% of the selected studies used public datasets, and the remaining used exclusive datasets. Several studies employed augmentation, scaling, and image normalization pre-processing techniques to minimize inconsistencies in breast cancer images. Several types of shallow and deep neural network architecture were employed to classify breast cancer using images. The convolutional neural network was utilized frequently to construct an effective breast cancer classification model. Some of the selected studies employed a pre-trained network or developed new deep neural networks to classify breast cancer. Most of the selected studies used accuracy and area-under-the-curve metrics followed by sensitivity, precision, and F-measure metrics to evaluate the performance of the developed breast cancer classification models. Finally, this review presented 10 open research challenges for future scholars who are interested to develop breast cancer classification models through various imaging modalities. This review could serve as a valuable resource for beginners on medical image classification and for advanced scientists focusing on deep learning-based breast cancer classification through different medical imaging modalities.