Medical image analysis plays a pivotal role in the evaluation of diseases, including screening, surveillance, diagnosis, and prognosis. Liver is one of the major organs responsible for key functions of metabolism, protein and hormone synthesis, detoxification, and waste excretion. Patients with advanced liver disease and Hepatocellular Carcinoma (HCC) are often asymptomatic in the early stages; however delays in diagnosis and treatment can lead to increased rates of decompensated liver diseases, late-stage HCC, morbidity and mortality. Ultrasound (US) is commonly used imaging modality for diagnosis of chronic liver diseases that includes fibrosis, cirrhosis and portal hypertension. In this paper, we first provide an overview of various diagnostic methods for stages of liver diseases and discuss the role of Computer-Aided Diagnosis (CAD) systems in diagnosing liver diseases. Second, we review the utility of machine learning and deep learning approaches as diagnostic tools. Finally, we present the limitations of existing studies and outline future directions to further improve diagnostic accuracy, as well as reduce cost and subjectivity, while also improving workflow for the clinicians.