Cancer is the second cause of mortality worldwide and it has been identified as a perilous disease. Breast cancer accounts for ∼20% of all new cancer cases worldwide, making it a major cause of morbidity and mortality. Mammography is an effective screening tool for the early detection and management of breast cancer. However, the identification and interpretation of breast lesions is challenging even for expert radiologists. For that reason, several Computer-Aided Diagnosis (CAD) systems are being developed to assist radiologists to accurately detect and/or classify breast cancer. This review examines the recent literature on the automatic detection and/or classification of breast cancer in mammograms, using both conventional feature-based machine learning and deep learning algorithms. The review begins with a comparison of algorithms developed specifically for the detection and/or classification of two types of breast abnormalities, micro-calcifications and masses, followed by the use of sequential mammograms for improving the performance of the algorithms. The available Food and Drug Administration (FDA) approved CAD systems related to triage and diagnosis of breast cancer in mammograms are subsequently presented. Finally, a description of the open access mammography datasets is provided and the potential opportunities for future work in this field are highlighted. The comprehensive review provided here can serve both as a thorough introduction to the field but also provide indicative directions to guide future applications.