Liver fibrosis is a histological hallmark of most chronic liver diseases, which can progress to cirrhosis and liver failure, and predisposes to hepatocellular carcinoma. Accurate diagnosis of liver fibrosis is necessary for prognosis, risk stratification, and treatment decision-making. Liver biopsy, the reference standard for assessing liver fibrosis, is invasive, costly, and impractical for surveillance and treatment response monitoring. Elastography offers a noninvasive, objective, and quantitative alternative to liver biopsy. This article discusses the need for noninvasive assessment of liver fibrosis and reviews the comparative advantages and limitations of ultrasound and magnetic resonance elastography techniques with respect to their basic concepts, acquisition, processing, and diagnostic performance. Variations in clinical contexts of use and common pitfalls associated with each technique are considered. In addition, current challenges and future directions to improve the diagnostic accuracy and clinical utility of elastography techniques are discussed. Level of Evidence: 5 Technical Efficacy Stage: 2 J. Magn. Reson. Imaging 2020;51:25-42.