The liver fulfils a plethora of vital functions and, due to their importance, liver dysfunction has life-threatening consequences. Liver disorders currently account for more than two million deaths annually worldwide and can be classified broadly into three groups, considering their onset and aetiology, as acute liver diseases, inherited metabolic disorders and chronic liver diseases. In the most advanced and severe forms leading to liver failure, liver transplantation is the only treatment available, which has many associated drawbacks, including a shortage of organ donors. Cell therapy via fully mature cell transplantation is an advantageous alternative that may be able to restore a damaged organ's functionality or serve as a bridge until regeneration can occur. Pioneering work has shown that transplanting adult hepatocytes can support liver recovery. However, primary hepatocytes cannot be grown extensively in vitro as they rapidly lose their metabolic activity. Therefore, different cell sources are currently being tested as alternatives to primary cells. Human pluripotent stem cell-derived cells, chemically induced liver progenitors, or 'liver' organoids, hold great promise for developing new cell therapies for acute and chronic liver diseases. This Review focuses on the advantages and drawbacks of distinct cell sources and the relative strategies to address different therapeutic needs in distinct liver diseases.