Malignant liver tumours include a wide range of primary and secondary tumours. Although surgery remains the mainstay of curative treatment, modern therapies integrate a variety of neoadjuvant and adjuvant strategies and have achieved dramatic improvements in survival. Extensive tumour loads, which have traditionally been considered unresectable, are now amenable to curative treatment through systemic conversion chemotherapies followed by a variety of interventions such as augmentation of the healthy liver through portal vein occlusion, staged surgeries or ablation modalities. Liver transplantation is established in selected patients with hepatocellular carcinoma but is now emerging as a promising option in many other types of tumour such as perihilar cholangiocarcinomas, neuroendocrine or colorectal liver metastases. In this Review, we summarize the available therapies for the treatment of malignant liver tumours, with an emphasis on surgical and ablative approaches and how they align with other therapies such as modern anticancer drugs or radiotherapy. In addition, we describe three complex case studies of patients with malignant liver tumours. Finally, we discuss the outlook for future treatment, including personalized approaches based on molecular tumour subtyping, response to targeted drugs, novel biomarkers and precision surgery adapted to the specific tumour.