Viral hepatitis was previously the most common cause of chronic liver disease. However, in recent years, nonalcoholic fatty liver disease (NAFLD) cases have been increasing, especially in developed countries. NAFLD is histologically characterized by fat, fibrosis, and inflammation in the liver, eventually leading to cirrhosis and hepatocellular carcinoma. Although biopsy is the gold standard for the assessment of the liver parenchyma, quantitative evaluation methods, such as ultrasound, CT, and MRI, have been reported to have good diagnostic performances. The quantification of liver fat, fibrosis, and inflammation is expected to be clinically useful in terms of the prognosis, early intervention, and treatment response for the management of NAFLD. The aim of this review was to discuss the basics and prospects of MRI-based tissue quantifications of the liver, mainly focusing on proton density fat fraction for the quantification of fat deposition, MR elastography for the quantification of fibrosis, and multifrequency MR elastography for the evaluation of inflammation.