In regenerative medicine and tissue engineering, the possibility to: (I) customize the shape and size of scaffolds, (II) develop highly mimicked tissues with a precise digital control, (III) manufacture complex structures and (IV) reduce the wastes related to the production process, are the main advantages of additive manufacturing technologies such as three-dimensional (3D) bioprinting. Specifically, this technique, which uses suitable hydrogel-based bioinks, enriched with cells and/or growth factors, has received significant consideration, especially in cartilage tissue engineering (CTE). In this field of interest, it may allow mimicking the complex native zonal hyaline cartilage organization by further enhancing its biological cues. However, there are still some limitations that need to be overcome before 3D bioprinting may be globally used for scaffolds’ development and their clinical translation. One of them is represented by the poor availability of appropriate, biocompatible and eco-friendly biomaterials, which should present a series of specific requirements to be used and transformed into a proper bioink for CTE. In this scenario, considering that, nowadays, the environmental decline is of the highest concerns worldwide, exploring naturally-derived hydrogels has attracted outstanding attention throughout the scientific community. For this reason, a comprehensive review of the naturally-derived hydrogels, commonly employed as bioinks in CTE, was carried out. In particular, the current state of art regarding eco-friendly and natural bioinks’ development for CTE was explored. Overall, this paper gives an overview of 3D bioprinting for CTE to guide future research towards the development of more reliable, customized, eco-friendly and innovative strategies for CTE.