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The most common liver malignancy is hepatocellular carcinoma (HCC), which is also associated with high mortality. Often HCC develops in a chronic liver disease setting, and early diagnosis as well as accurate screening of high-risk patients is crucial for appropriate and effective management of these patients. While imaging characteristics of HCC are well-defined in the diagnostic phase, challenging cases still occur, and current prognostic and predictive models are limited in their accuracy. Radiomics and machine learning (ML) offer new tools to address these issues and may lead to scientific breakthroughs with the potential to impact clinical practice and improve patient outcomes. In this review, we will present an overview of these technologies in the setting of HCC imaging across different modalities and a range of applications. These include lesion segmentation, diagnosis, prognostic modeling and prediction of treatment response. Finally, limitations preventing clinical application of radiomics and ML at the present time are discussed, together with necessary future developments to bring the field forward and outside of a purely academic endeavor.