Hepatocellular carcinoma (HCC) is the most prevalent primary liver cancer and a leading cause of cancer-related deaths worldwide. Ninety percent of HCC cases arise from cirrhosis, during which liver cells undergo chronic cycles of necrosis and regeneration. The complex genomic landscape of HCC has been extensively investigated to draw correlations between recurrently mutated pathways and patient prognosis. However, our limited success with targeted therapy shows that knowing the presence of somatic mutations alone is insufficient for us to gauge the full spectrum of their functional consequences in the context of tumor evolution. In addition, the current molecular classification of HCC offers little information on the relationship between the molecular features and immunological properties of HCC tumors and their immune microenvironment. This review introduces current challenges and advancements made in HCC surveillance, diagnosis, and treatment. We also discuss the suite of HCC-associated genetic changes and describe recent studies that provide evidence for an evolving functional model and its implications for understanding and targeting HCC progression.