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Nowadays it is widely accepted that Artificial Intelligence (AI) is significantly influencing a large number of domains, including railways. In this paper, we present a systematic literature review of the current state-of-the-art of AI in railway transport. In particular, we analysed and discussed papers from a holistic railway perspective, covering sub-domains such as maintenance and inspection, planning and management, safety and security, autonomous driving and control, revenue management, transport policy, and passenger mobility. This review makes an initial step towards shaping the role of AI in future railways and provides a summary of the current focuses of AI research connected to rail transport. We reviewed about 139 scientific papers covering the period from 2010 to December 2020. We found that the major research efforts have been put in AI for rail maintenance and inspection, while very limited or no research has been found on AI for rail transport policy and revenue management. The remaining sub-domains received mild to moderate attention. AI applications are promising and tend to act as a game-changer in tackling multiple railway challenges. However, at the moment, AI research in railways is still mostly at its early stages. Future research can be expected towards developing advanced combined AI applications (e.g. with optimization), using AI in decision making, dealing with uncertainty and tackling newly rising cybersecurity challenges.