Acute kidney injury (AKI) is a common complication of cirrhosis, burdened by high morbidity and mortality rates and progression to chronic kidney disease. Hepatorenal syndrome (HRS) is a peculiar type of functional AKI observed in cirrhotic patients with ascites. HRS diagnosis is still clinical, once pre-renal azotemia and intrinsic kidney damage have been excluded by applying well-established and internationally adopted criteria. HRS is considered reversible because of the absence of intrinsic renal damage. However, HRS reversibility has been questioned, due to the lack of response to treatment with vasoconstrictors plus albumin in a relevant percentage of patients and to the persistence of renal dysfunction in HRS patients who underwent liver transplantation (LT). Indeed, LT is the only ultimate treatment, as it solves both liver failure and portal hypertension. Thus, the presence of renal damage in HRS can be hypothesized. In this scenario, neutrophil gelatinase-associated lipocalin (NGAL), one of the most promising biomarkers, may help in characterizing the type of renal injury, distinguishing between HRS and acute tubular necrosis. This review gathers the available evidence in favor and against the presence of structural lesions in HRS in terms of either renal histology and urinary biomarkers with a particular focus on NGAL. The ability to properly characterize which component of renal dysfunction prevails – functional rather than structural – entails a relevant clinical impact for the treatment of these patients, both in terms of medical therapy and liver vs. combined liver-kidney transplantation.