Extreme ultraviolet (EUV) radiation is a key technology for material science, attosecond metrology, and lithography. Here, we experimentally demonstrate metasurfaces as a superior way to focus EUV light. These devices exploit the fact that holes in a silicon membrane have a considerably larger refractive index than the surrounding material and efficiently vacuum-guide light with a wavelength of ~50 nanometers. This allows the transmission phase at the nanoscale to be controlled by the hole diameter. We fabricated an EUV metalens with a 10-millimeter focal length that supports numerical apertures of up to 0.05 and used it to focus ultrashort EUV light bursts generated by high-harmonic generation down to a 0.7-micrometer waist. Our approach introduces the vast light-shaping possibilities provided by dielectric metasurfaces to a spectral regime that lacks materials for transmissive optics.