Biofabrication is enriching the tissue engineering field with new ways of producing structurally organized complex tissues. Among the numerous bioinks under investigation, hyaluronic acid (HA) and its derivatives stand out for their biological relevance, cytocompatibility, shear-thinning properties, and potential to fine-tune the desired properties with chemical modification. In this paper, we review the recent advances on bioinks containing HA. The available literature is presented based on subjects including the rheological properties in connection with printability, the chemical strategies for endowing HA with the desired properties, the clinical application, the most advanced preclinical studies, the advantages and limitations in comparison with similar biopolymer-based bioinks, and future perspectives.