The liver is the second-largest organ in the human body and is essential for digesting food and removing toxic substances. Viruses, obesity, alcohol use, and other factors can damage the liver and cause liver disease. The diagnosis of liver disease used to depend on the clinical experience of doctors, which made it subjective, difficult, and time-consuming. Deep learning has made breakthroughs in various fields; thus, there is a growing interest in using deep learning methods to solve problems in liver research to assist doctors in diagnosis and treatment. In this paper, we provide an overview of deep learning in liver research using 139 papers from the last 5 years. We also show the relationship between data modalities, liver topics, and applications in liver research using Sankey diagrams and summarize the deep learning methods used for each liver topic, in addition to the relations and trends between these methods. Finally, we discuss the challenges of and expectations for deep learning in liver research.