Drug-induced liver injury (DILI) is a common reason for the withdrawal of a drug from the market. Early assessment of DILI risk is an essential part of drug development, but it is rendered challenging prior to clinical trials by the complex factors that give rise to liver damage. Artificial intelligence (AI) approaches, particularly those building on machine learning, range from random forests to more recent techniques such as deep learning, and provide tools that can analyze chemical compounds and accurately predict some of their properties based purely on their structure. This article reviews existing AI approaches to predicting DILI and elaborates on the challenges that arise from the as yet limited availability of data. Future directions are discussed focusing on rich data modalities, such as 3D spheroids, and the slow but steady increase in drugs annotated with DILI risk labels.