We propose to observe a selection of RV Tauri stars with the SWS. We will address the following questions: (i) what is the nature of the cool outer (AGB) shell of RV Tauri stars? (ii) what is the origin of the peculiar 'silicate' feature seen in many RV Tauri stars? (iii) what is the distribution of dust around RV Tauri stars? (iv) is there evidence for iron oxide grains in the envelopes of RV Tauri stars, which may have originated in the AGB progenitor? SWS observations of RV Tauri stars will provide answers to such questions and will lead to important new information on the evolutionary history of these poorly-understood objects.