Biofabrication for tissue engineering and regenerative medicine is a rapidly evolving field that incorporates bioprinting or bioassembly for the development of biologically functional products with structural organization using cells, bioactive molecules, and biomaterials. Bioprinting is a biofabrication technology that utilizes biomaterials, living cells, and supporting materials, called bioink, to generate three-dimensional tissue constructs. Bioprinting offers several advantages over traditional scaffolding and microengineering methods such as precise architecture control, high reproducibility, and versatility. The ideal bioink should possess appropriate structural, mechanical, gelation, rheological, chemical, biological, degradation, and biomimetic properties for the desired application of the final product. Several natural and synthetic bioinks have been developed and this review has focused on conductive nanomaterials that have been used in combination with hydrogel materials for bioink synthesis.