Background: Mammographic-mass segmentation and classification are crucial for early diagnosis of breast cancer. Traditional machine learning approaches have shown promising results for both mass segmentation and classification but deep learning approaches have demonstrated superior performance. Objective: This review focuses on both traditional and deep learning-based machine learning techniques employed in mammographic-mass segmentation, localization, and classification techniques. It traces the evolution from classical machine learning algorithms to deep learning for mass detection and classification tasks. Methods: The mass segmentation and detection methods discussed in this review are built on the principles such as region-growing, contour-based approaches, and thresholding, as well as modern deep learning models like U-Net, YOLO, and R-CNN. For mass classification, traditional classifiers like Artificial Neural Network, Support Vector Machine, and their deep learning counter parts are discussed. Results: Traditional segmentation methods often struggle with complex mammograms with dense tissues or indistinct mass boundaries. In contrast deep learning has brought remarkable improvement in segmentation, localization of masses as well mass in classification. Conclusion: Deep learning-based approaches are proven to be more efficient in segmentation and classification of mammographic mass compared to the traditional approaches. Deep learning can efficiently extract features from mammograms and may fully integrate into the breast cancer diagnosis.