Nonalcoholic fatty liver disease (NAFLD) is the major contributor to the global burden of chronic liver diseases and ranges from simple and reversible steatosis to nonalcoholic steatohepatitis (NASH), which may progress into cirrhosis and hepatocellular carcinoma (HCC). HCC represents the most common liver cancer, and it is a leading cause of death worldwide with an increasing trend for the future. Due to late diagnosis, non-responsiveness to systemic therapy, and high cancer heterogeneity, the treatment of this malignancy is challenging. To date, liver biopsy and ultrasound (US) are the gold standard procedures for HCC diagnosis and surveillance, although they are not suitable for mass screening. Therefore, it is impelling to find new, less invasive diagnostic strategies able to detect HCC at an early stage as well as monitor tumor progression and recurrence. Common and rare inherited variations that boost the switching from NASH to liver cancer may help to predict tumor onset. Furthermore, epigenetic changes which reflect intertumoral heterogeneity occur early in tumorigenesis and are highly stable under pathologic conditions. The severity of hepatic injuries can be detected through the analysis of cell circulating tumor DNAs (ctDNAs), microRNAs (miRNAs), and noncoding RNAs (ncRNAs), which are involved in several pathological processes that feature cancer, including cell growth, survival, and differentiation, thus representing appealing biomarkers for HCC. Therefore, this review discusses the current options for HCC surveillance, focusing on the role of genetic and epigenetic biomarkers as new strategies to refine HCC management.