Refraction is a well-known optical phenomenon that alters the direction of light waves propagating through matter. Microscopes, lenses and prisms based on refraction are indispensable tools for controlling light beams at visible, infrared, ultraviolet and X-ray wavelengths(1). In the past few decades, a range of extreme-ultraviolet and soft-X-ray sources has been developed in laboratory environments(2-4) and at large-scale facilities(5,6). But the strong absorption of extreme-ultraviolet radiation in matter hinders the development of refractive lenses and prisms in this spectral region, for which reflective mirrors and diffractive Fresnel zone plates(7) are instead used for focusing. Here we demonstrate control over the refraction of extreme-ultraviolet radiation by using a gas jet with a density gradient across the profile of the extreme-ultraviolet beam. We produce a gas-phase prism that leads to a frequency-dependent deflection of the beam. The strong deflection near to atomic resonances is further used to develop a deformable refractive lens for extreme-ultraviolet radiation, with low absorption and a focal length that can be tuned by varying the gas pressure. Our results open up a route towards the transfer of refraction-based techniques, which are well established in other spectral regions, to the extreme-ultraviolet domain.