Structures of a family of new hydrated and anhydrous perrhenates of lead and strontium have been determined. Sr(ReO4)2·H2O is isostructural to Ce(CrO4)2·H2O and Th(CrO4)2·H2O; Pb(ReO4)2·2H2O is analogous to Sr(ReO4)2·2H2O and Pb(TcO4)2·2H2O. The compounds Sr(ReO4)2·6H2O, Pb(ReO4)Cl·2H2O, and {Pb4(OH)4}(ReO4)4·H2O correspond to new structural architectures. We discuss the similarities and differences in the crystal structures of relatively simple inorganic salts containing tetrahedral oxoanions based on d-elements (MnO4−, TcO4−, ReO4−, CrO42−, and MoO42−); the analogies to tetrahedral p-based hydrido- or fluoroanions (BF4− and AlH4−) exist but are as yet rare.