This review article focuses on sepiolite fibrous clay mineral, which has been selected here as an example of an ancient inorganic natural material that is currently receiving much attention as excellent candidate for advanced materials and applications. Sepiolite clay is an abundant hydrated magnesium silicate whose crystal structure determines the presence of nanoporous cavities as well as large surface and rheological properties of great interest for the further design of functional materials. The present work introduces and discusses the relationship between aspects of this clay, in terms of its structural and morphological organization, and its physicochemical characteristics from which emerging applications arise. One of the sections is devoted to describe current industrial applications of commercially available sepiolite-based materials. As sepiolite can be considered a nanomaterial by itself, approaches including its controlled chemical and physical modifications intended to develop new advanced inorganic and hybrid nanostructured materials provided with pre-designed functionalities. Among them, polymer nanocomposites that include bionanocomposites and carbon-sepiolite nanomaterials, materials for adsorption of pollutants, functionalization with magnetic nanoparticles, active phase of sensors and DNA support for gene transfer are some of the examples that we refer to in the present review article.