Retrospective studies have shown artificial intelligence (AI) algorithms can match as well as enhance radiologist's performance in breast screening. These tools can facilitate tasks not feasible by humans such as the automatic triage of patients and prediction of treatment outcomes. Breast imaging faces growing pressure with the exponential growth in imaging requests and a predicted reduced workforce to provide reports. Solutions to alleviate these pressures are being sought with an increasing interest in the adoption of AI to improve workflow efficiency as well as patient outcomes. Vast quantities of data are needed to test and monitor AI algorithms before and after their incorporation into healthcare systems. Availability of data is currently limited, although strategies are being devised to harness the data that already exists within healthcare institutions. Challenges that underpin the realisation of AI into everyday breast imaging cannot be underestimated and the provision of guidance from national agencies to tackle these challenges, taking into account views from a societal, industrial and healthcare prospective is essential. This review provides background on the evaluation and use of AI in breast imaging in addition to exploring key ethical, technical, legal and regulatory challenges that have been identified so far.