Sepiolite and palygorskite are natural microfibrous clay minerals whose particular structural, morphological and textural features are useful for the preparation of a wide variety of advanced nanostructured materials, essentially regarding their ability to render nanocomposite materials. The silanol groups located on the external surface of these silicates and their surface electrical charge are the centers for interactions with biopolymers, such as polysaccharides, proteins, lipids and nucleic acids. In the present review we introduce recent results from sepiolite- and palygorskite-based bionanocomposites showing the interest of these silicates compared to lamellar clays for diverse applications such as bioplastics and membranes, uses in biomedicine as drug delivery systems and adjuvants of vaccines as well as in tissue engineering. Other applications here discussed focus on environmental purposes, the use of bionanocomposites as components of sensor devices and bioreactors and as source of supported graphene.