Applications of natural hyaluronic acid (HYH) for the fabrication of organic–inorganic composites for biomedical applications are described. Such composites combine unique functional properties of HYH with functional properties of hydroxyapatite, various bioceramics, bioglass, biocements, metal nanoparticles, and quantum dots. Functional properties of advanced composite gels, scaffold materials, cements, particles, films, and coatings are described. Benefiting from the synergy of properties of HYH and inorganic components, advanced composites provide a platform for the development of new drug delivery materials. Many advanced properties of composites are attributed to the ability of HYH to promote biomineralization. Properties of HYH are a key factor for the development of colloidal and electrochemical methods for the fabrication of films and protective coatings for surface modification of biomedical implants and the development of advanced biosensors. Overcoming limitations of traditional materials, HYH is used as a biocompatible capping, dispersing, and structure-directing agent for the synthesis of functional inorganic materials and composites. Gel-forming properties of HYH enable a facile and straightforward approach to the fabrication of antimicrobial materials in different forms. Of particular interest are applications of HYH for the fabrication of biosensors. This review summarizes manufacturing strategies and mechanisms and outlines future trends in the development of functional biocomposites.