Hyaluronic acid (HA) is a natural polyelectrolyte abundant in mammalian connective tissues, such as cartilage and skin. Both endogenous and exogenous HA produced by fermentation have similar physicochemical, rheological, and biological properties, leading to medical and dermo-cosmetic products. Chemical modifications such as cross-linking or conjugation in target groups of the HA molecule improve its properties and in vivo stability, expanding its applications. Currently, HA-based scaffolds and matrices are of great interest in tissue engineering and regenerative medicine. However, the partial oxidation of the proximal hydroxyl groups in HA to electrophilic aldehydes mediated by periodate is still rarely investigated. The introduced aldehyde groups in the HA backbone allow spontaneous cross-linking with adipic dihydrazide (ADH), thermosensitivity, and noncytotoxicity to the hydrogels, which are advantageous for medical applications. This review provides an overview of the physicochemical properties of HA and its usual chemical modifications to better understand oxi-HA/ADH hydrogels, their functional properties modulated by the oxidation degree and ADH concentration, and the current clinical research. Finally, it discusses the development of biomaterials based on oxi-HA/ADH as a novel approach in tissue engineering and regenerative medicine.