Chronic liver diseases (CLDs) are becoming increasingly more prevalent in modern society. The use of imaging techniques for early detection, such as magnetic resonance imaging (MRI), is crucial in reducing the impact of these diseases on healthcare systems. Artificial intelligence (AI) algorithms have been shown over the past decade to excel at image-based analysis tasks such as detection and segmentation. When applied to liver MRI, they have the potential to improve clinical decision making, and increase throughput by automating analyses. With Liver diseases becoming more prevalent in society, the need to implement these techniques to utilize liver MRI to its full potential, is paramount. In this review, we report on the current methods and applications of AI methods in liver MRI, with a focus on machine learning and deep learning methods. We assess four main themes of segmentation, classification, image synthesis and artefact detection, and their respective potential in liver MRI and the wider clinic. We provide a brief explanation of some of the algorithms used and explore the current challenges affecting the field. Though there are many hurdles to overcome in implementing AI methods in the clinic, we conclude that AI methods have the potential to positively aid healthcare professionals for years to come.