Hepatocellular carcinoma (HCC) represents a global health challenge, and ranks among one of the most prevalent and deadliest cancers worldwide. Therapeutic advances have expanded the treatment armamentarium for patients with advanced HCC, but obstacles remain. Precision oncology, which aims to match specific therapies to patients who have tumours with particular features, holds great promise. However, its implementation has been hindered by the existence of numerous 'HCC influencers' that contribute to the high inter-patient heterogeneity. HCC influencers include tumour-related characteristics, such as genetic alterations, immune infiltration, stromal composition and aetiology, and patient-specific factors, such as sex, age, germline variants and the microbiome. This Review delves into the intricate world of HCC, describing the most innovative model systems that can be harnessed to identify precision and/or personalized therapies. We provide examples of how different models have been used to nominate candidate biomarkers, their limitations and strategies to optimize such models. We also highlight the importance of reproducing distinct HCC influencers in a flexible and modular way, with the aim of dissecting their relative contribution to therapy response. Next-generation HCC models will pave the way for faster discovery of precision therapies for patients with advanced HCC.