Studies have shown that the use of artificial intelligence can reduce errors in medical image assessment. The diagnosis of breast cancer is an essential task; however, diagnosis can include 'detection' and 'interpretation' errors. Studies to reduce these errors have shown the feasibility of using convolution neural networks (CNNs). This narrative review presents recent studies in diagnosing mammographic malignancy investigating the accuracy and reliability of these CNNs. Databases including ScienceDirect, PubMed, MEDLINE, British Medical Journal and Medscape were searched using the terms 'convolutional neural network or artificial intelligence', 'breast neoplasms [MeSH] or breast cancer or breast carcinoma' and 'mammography [MeSH Terms]'. Articles collected were screened under the inclusion and exclusion criteria, accounting for the publication date and exclusive use of mammography images, and included only literature in English. After extracting data, results were compared and discussed. This review included 33 studies and identified four recurring categories of studies: the differentiation of benign and malignant masses, the localisation of masses, cancer-containing and cancer-free breast tissue differentiation and breast classification based on breast density. CNN's application in detecting malignancy in mammography appears promising but requires further standardised investigations before potentially becoming an integral part of the diagnostic routine in mammography. 134