Three-dimensional (3D) bioprinting has played an increasingly crucial role in the manufacturing of organized complex tissues and organs, which has shown tremendous potential in the field of tissue engineering. Extrusion-based bioprinting takes advantage of its competitive pricing and flexibility to print various biomaterials, and it has now developed into one of the most used printing techniques. However, extruding soft hydrogels, also known as bioinks, often leads to poor fidelity when printed in air. As an emerging printing approach, 3D embedded bioprinting deposits bioinks not on a platform but into a support bath, preventing constructs from settling and collapsing. This review discusses the challenges faced in the traditional 3D bioprinting of soft or low-viscosity bioinks and the changes brought by embedded bioprinting as an emerging solution. Particular focus is given to the progress of hydrogels used as bioinks and support baths. Finally, we highlight the challenges involved in this process and look forward to the prospects of this technology.