Nanocomposite (NC) hydrogels, organic-inorganic hybrid materials, are of great interest as artificial three-dimensional (3D) biomaterials for biomedical applications. NC hydrogels are prepared in water by chemically or physically cross-linking organic polymers with nanomaterials (NMs). The incorporation of hard inorganic NMs into the soft organic polymer matrix enhances the physical, chemical, and biological properties of NC hydrogels. Therefore, NC hydrogels are excellent candidates for artificial 3D biomaterials, particularly in tissue engineering applications, where they can mimic the chemical, mechanical, electrical, and biological properties of native tissues. A wide range of functional NMs and synthetic or natural organic polymers have been used to design new NC hydrogels with novel properties and tailored functionalities for biomedical uses. Each of these approaches can improve the development of NC hydrogels and, thus, provide advanced 3D biomaterials for biomedical applications.