Bioinks are employed in the fabrication of 3D scaffolds containing cells and macromolecules that can be applied in regenerative medicine. The use of such bioinks facilitates the controlled introduction and localization of macromolecules, bioactives and cells for the biofabrication of living tissues. To enable the successful preparation of the bioinks, strategies involving the use of so-called cross linkers, which may be ionic, chemical, photo-etc. based, are employed. Some of these strategies such as the use of glutaraldehyde as a crosslinker or harsh crosslinking conditions may however compromise the cytocompatibility of the bioink. To circumvent this challenge, the employment of click chemistry technology has been proposed. This is because, click chemistry can enable the preparation of well-tuned bioinks in the absence of problematic cross-linkers, while ensuring that favorable gelation rate, degradation rate, and cell viability properties of the bioinks are not compromised. Indeed, the bio-orthogonal nature of click chemistry has been suggested to enhance the maintenance of high cell viability in scaffolds. In this regard, the current study explored the potential of using different click chemistries in specific bioprinting techniques. Major bioinks produced using click chemistry were also identified, with existing challenges and future trends discussed. It is anticipated that this review will be invaluable to the tissue engineering field by providing an important resource for bioengineers and a basis of future decisions regarding the selection of the preferred click chemistry for specific bioink functionalities.