HCV eradication by antiviral treatment reduces but does not eliminate HCC risk. Patients with established cirrhosis require HCC surveillance "indefinitely" after sustained virologic response (SVR) because they appear to have a high risk of HCC even many years after SVR. Patients without established or known cirrhosis may still require surveillance after SVR if they have a sufficiently high HCC risk. In all patients who achieve SVR, the key question is how we can reliably estimate HCC risk, and the change in HCC risk over time, to determine whether the patient might benefit from HCC surveillance. HCC risk is one of the most important factors that should inform decisions of whether and how to screen for HCC. Promising strategies for estimating HCC risk include simplified scoring systems (such as fibrosis-4), liver elastography and multivariable HCC risk calculators. Such tools may enable risk stratification and individualised, risk-based surveillance strategies ("precision HCC screening") in the future.