Screening for breast cancer with mammography has been introduced in various countries over the last 30 years, initially using analog screen-film-based systems and, over the last 20 years, transitioning to the use of fully digital systems. With the introduction of digitization, the computer interpretation of images has been a subject of intense interest, resulting in the introduction of computer-aided detection (CADe) and diagnosis (CADx) algorithms in the early 2000's. Although they were introduced with high expectations, the potential improvement in the clinical realm failed to materialize, mostly due to the high number of false positive marks per analyzed image. In the last five years, the artificial intelligence (AI) revolution in computing, driven mostly by deep learning and convolutional neural networks, has also pervaded the field of automated breast cancer detection in digital mammography and digital breast tomosynthesis. Research in this area first involved comparison of its capabilities to that of conventional CADe/CADx methods, which quickly demonstrated the potential of this new technology. In the last couple of years, more mature and some commercial products have been developed, and studies of their performance compared to that of experienced breast radiologists are showing that these algorithms are on par with human-performance levels in retrospective data sets. Although additional studies, especially prospective evaluations performed in the real screening environment, are needed, it is becoming clear that AI will have an important role in the future breast cancer screening realm. Exactly how this new player will shape this field remains to be determined, but recent studies are already evaluating different options for implementation of this technology. The aim of this review is to provide an overview of the basic concepts and developments in the field AI for breast cancer detection in digital mammography and digital breast tomosynthesis. The pitfalls of conventional methods, and how these are, for the most part, avoided by this new technology, will be discussed. Importantly, studies that have evaluated the current capabilities of AI and proposals for how these capabilities should be leveraged in the clinical realm will be reviewed, while the questions that need to be answered before this vision becomes a reality are posed.