The interaction of waves with inhomogeneous media leads to the natural focusing of light, the channelling of waves into stable caustics such as the pattern of sunlight seen at the bottom of a rippled swimming pool. These effects are also found in surface acoustic wave devices, gravitational lensing of galaxies, and even the search for dark matter in the universe. We have extended natural focusing to x-rays, observing x-ray caustics for the first time in topographs of ferroelectric domains in lithium niobate in an external electric field. Controlling the voltage across a wafer with domains of reversed polarity induces subtle perturbations to the local crystal planes, producing dramatic yet reversible variations in the reflected x-ray images. Ray-tracing simulation reveals a catastrophic discontinuity of ray density, causing the bright caustic focal lines. Image analysis permits new insights into domain boundary strains and their effect on ferroelectric properties. Similar focusing seen from an unpoled specimen suggests a field-induced polarization of unknown origin. Controlled focusing could be extended to designed domain patterns, such as periodically-poled structures. In addition to being a powerful probe of microstructure in ferroelectrics, these caustic images suggest new opportunities for voltage-controlled ferroelectric optics for x-rays.