Considerable effort has been directed toward developing new types of artificial materials known now as photonic crystals and metamaterials. Even though the initial focus was not on creating a spatially varying refractive index, it was soon realized that such materials can be fabricated with an index gradient in one or more dimensions. In this chapter, we focus on the novel GRIN devices whose design is based on photonic crystals and metamaterials. Section 10.1 introduces the basic concepts needed to understand the physics behind these two types of materials. Section 10.2 is devoted to GRIN structures based on the concept of photonic crystals. Metamaterials designed with an index gradient are discussed in Section 10.3. The focus of Section 10.4 is on a subgroup of metamaterials, known as metasurfaces, which contain nanoscale objects made with dielectric or metallic materials and are thinner than the wavelength of radiation they are intended for.