Non-alcoholic fatty liver disease (NAFLD) comprises a wide spectrum of hepatic disorders, from simple steatosis to hepatic necro-inflammation leading to non-alcoholic steatohepatitis (NASH). Although the prevalence of these multifactorial pathologies is continuously increasing in the population, there is still not an established methodology for their treatment other than weight loss and a change in lifestyle habits, such as a hypocaloric diet and physical exercise. In this framework, there is increasing evidence that several food bioactives and dietary patterns are effective for reversing and preventing the onset of these pathologies. Some studies have claimed that better responses are obtained when treatments are performed under a multifaceted approach, using different bioactive compounds that act against complementary targets. Thus, in this work, current strategies for treating NAFLD and NASH based on multi-ingredient-based supplements or the Mediterranean diet, a dietary pattern rich in bioactive compounds, are reviewed. Furthermore, the usefulness of omics techniques to design effective multi-ingredient nutritional interventions and to predict and monitor their response against these disorders is also discussed.