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In this paper, we present a class of imaging systems, called radial imaging systems, that capture a scene from a large number of view-points within a single image, using a camera and a curved mirror. These systems can recover scene properties such as geometry, reflectance, and texture. We derive analytic expressions that describe the properties of a complete family of radial imaging systems, including their loci of viewpoints, fields of view, and resolution characteristics. We have built radial imaging systems that, from a single image, recover the frontal 3D structure of an object, generate the complete texture map of a convex object, and estimate the parameters of an analytic BRDF model for an isotropic material. In addition, one of our systems can recover the complete geometry of a convex object by capturing only two images. These results show that radial imaging systems are simple, effective, and convenient devices for a wide range of applications in computer graphics and computer vision.