The study of extended, cold dust envelopes surrounding R Coronae Borealis (RCB) stars began with their discovery by the Infrared Astronomical Satellite. RCB stars are carbon-rich supergiants characterized by their extreme hydrogen deficiency and their irregular and spectacular declines in brightness (up to 9 mag). We have analyzed new and archival Spitzer Space Telescope and Herschel Space Observatory data of the envelopes of seven RCB stars to examine the morphology and investigate the origin of these dusty shells. Herschel, in particular, has revealed the first-ever bow shock associated with an RCB star with its observations of SU Tauri. These data have allowed the assembly of the most comprehensive spectral energy distributions (SEDs) of these stars with multiwavelength data from the ultraviolet to the submillimeter. Radiative transfer modeling of the SEDs implies that the RCB stars in this sample are surrounded by an inner warm (up to 1200 K) and an outer cold (up to 200 K) envelope. The outer shells are suggested to contain up to 10‑3 M ⊙ of dust and have existed for up to 105 years depending on the expansion rate of the dust. This age limit indicates that these structures have most likely been formed during the RCB phase.