Three-dimensional (3D)-printed in vitro tissue models have been used in various biomedical fields owing to numerous advantages such as enhancements in cell response and functionality. In liver tissue engineering, several studies have been reported using 3D-printed liver tissue models with improved cellular responses and functions in drug screening, liver disease, and liver regenerative medicine. However, the application of conventional single-component bioinks for the printing of 3D in vitro liver constructs remains problematic because of the complex structural and physiological characteristics of the liver. The use of multicomponent bioinks has become an attractive strategy for bioprinting 3D functional in vitro liver tissue models because of the various advantages of multicomponent bioinks, such as improved mechanical properties of the printed tissue construct and cell functionality. Therefore, it is essential to review various 3D bioprinting techniques and multicomponent hydrogel bioinks proposed for liver tissue engineering to suggest future directions for liver tissue engineering. Accordingly, we herein review multicomponent bioinks for 3D-bioprinted liver tissues. We first describe the fabrication methods capable of printing multicomponent bioinks and introduce considerations for bioprinting. We subsequently categorize and evaluate the materials typically utilized for multicomponent bioinks based on their characteristics. In addition, we also review recent studies for the application of multicomponent bioinks to fabricate in vitro liver tissue models. Finally, we discuss the limitations of current studies and emphasize aspects that must be resolved to enhance the future applicability of such bioinks.