A head-mounted display may include a display system and an optical system in a housing. The display system may have displays that produce images. Positioners may be used to move the displays relative to the eye positions of a user's eyes. An adjustable optical system may include tunable lenses such as tunable cylindrical liquid crystal lenses. The displays may be viewed through the lenses when the user's eyes are at the eye positions. A sensor may be incorporated into the head-mounted display to measure refractive errors in the user's eyes. The sensor may include waveguides and volume holograms, and a camera for gathering light that has reflected from the retinas of the user's eyes. Viewing comfort may be enhanced by adjusting display positions relative to the eye positions and/or by adjusting lens settings based on the content being presented on the display and/or measured refractive errors.