We present a comprehensive examination of Jupiter's "gossamer" rings based on images from Voyager, Galileo, the Hubble Space Telescope and the W.M. Keck Telescope. We compare our results to the simple dynamical model of Burns et al. [Burns, J.A., Showalter, M.R., Hamilton, D.P., Nicholson, P.D., de Pater, I., Ockert-Bell, M., Thomas, P., 1999. Science 284, 1146-1150] in which dust is ejected from Amalthea and Thebe and then evolves inward under Poynting-Robertson drag. The ring follows many predictions of the model rather well, including a linear reduction in thickness with decreasing radius. However, some deviations from the model are noted. For example, additional material appears to be concentrated just interior to the orbits of the two moons. At least in the case of Amalthea's ring, that material is in the same orbital plane as Amalthea's inclined orbit and may be trapped at the Lagrange points. Thebe's ring shows much larger vertical excursions from the model, which may be related to perturbations by several strong Lorentz resonances. Photometry is consistent with the dust obeying a relatively flat power-law size distribution, very similar to dust in the main ring. However, the very low backscatter reflectivity of the ring, and the flat phase curve of the ring at low phase angles, require that the ring be composed of distinctly non-spherical particles.