Three-dimensional (3D) extrusion-based bioprinting is widely used in tissue engineering and regenerative medicine to create cell-incorporated constructs or scaffolds based on the extrusion technique. One critical issue in 3D extrusion-based bioprinting is printability or the capability to form and maintain reproducible 3D scaffolds from bioink (a mixture of biomaterials and cells). Research shows that printability can be affected by many factors or parameters, including those associated with the bioink, printing process, and scaffold design, but these are far from certain. This review highlights recent developments in the printability assessment of extrusion-based bioprinting with a focus on the definition of printability, printability measurements and characterization, and printability-affecting factors. Key issues and challenges related to printability are also identified and discussed, along with approaches or strategies for improving printability in extrusion-based bioprinting.