Liver cancer has high incidence and mortality globally. Artificial intelligence (AI) has advanced rapidly, influencing cancer care. AI systems are already approved for clinical use in some tumour types (for example, colorectal cancer screening). Crucially, research demonstrates that AI can analyse histopathology, radiology and natural language in liver cancer, and can replace manual tasks and access hidden information in routinely available clinical data. However, for liver cancer, few of these applications have translated into large-scale clinical trials or clinically approved products. Here, we advocate for the incorporation of AI in all stages of liver cancer management. We present a taxonomy of AI approaches in liver cancer, highlighting areas with academic and commercial potential, and outline a policy for AI-based liver cancer management, including interdisciplinary training of researchers, clinicians and patients. The potential of AI in liver cancer is immense, but effort is required to ensure that AI can fulfil expectations.