Soft materials, such as hydrogels, are used as scaffolds in tissue engineering and regenerative medicine to help tissues regenerate and heal. Recently, supramolecular hydrogels, based on non-covalent interactions, have grown in popularity, especially in the development of materials for biomedical use. Their potential lies in the dynamic, reversible and temporary nature of their crosslinks, which can make them responsive to stimuli, injectable and suitable for 3D printing. Such versatility and processability is important when developing new biomaterials for drug delivery or as implantable scaffolds. The behavior and properties of such hydrogels are different compared to those of chemically crosslinked hydrogels. In this review, we give an overview on supramolecular hydrogels which contain hyaluronic acid (HA) as one of the building blocks. HA is particularly interesting, due to its hydrophilicity, biofunctionality and ease of chemical modification. Specifically, we focus on HA-based hydrogels that make use of hydrogen bonding, hydrophobic interactions, electrostatic interactions, metal–ion coordination and guest–host interactions, and are intended for applications in the biomedical field, with potential for clinical translation.