The creation of bioinks that can both support cells during the fabrication process and lead to advanced tissue function post-processing remains a challenge. If the tissue engineering community wishes to unlock the potential of 3D biofabrication techniques, new materials must be designed to meet these needs. In our lab, we take a look at new strategies with dynamic hydrogels as a potential solution to the demands of both fabrication and tissue formation. Recently, we have shown the ability to engineer shear-thinning and self-healing hydrogels utilizing dynamic (dynamic covalent and supramolecular) chemistry with rationally controllable mechanical properties. These viscoelastic materials are able to be 3D bioprinted, and offer unique opportunities to control cell behavior or improve culture conditions. Combined, these strategies show a potential path forward for the design of next-generation bioinks and tissue engineering hydrogels.