Hyperbolic media exhibit unparalleld properties, e.g, as light absorbers in photovoltaics and photonics, as superlenses in far-field imaging, as subwavelength light concentrators in nanolithography, or as novel materials in emission engineering. With the advent of optical metamaterials, deliberate design of material properties became possible. However, inadvertent variability in fabrication techniques and other factors limit performance characteristics of man-made hyperbolic materials. Here, we draw attention to a class of natural hyperbolic materials, the tetradymites. From generalized spectroscopic ellipsometry we extract the dielectric tensor components and find hyperbolic behavior in Bi2Se3 and Bi2Te3 in the near-infrared to visible spectrum. Previously, natural hyperbolic media were known only in the far-infrared spectral range. As possible applications of tetradymites we discuss superlenses for near-field microscopy and far-field isoindex filters. Solid solutions of tetradymites are likely tunable in operational wavelength from the infrared to the visible, complementing hyperbolic metamaterials.