Minerals with sulfate anions are one of the most diverse classes. More than 400 minerals containing sulfate anion are known to date. Most of known anhydrous sulfates have relatively simple chemical composition and structural architecture. In contrast, hydrated sulfate minerals have more complex compositions and structures. Most of the anhydrous sulfates are highly soluble compounds and unstable in humid atmosphere, namely, sulfates of alkali and alkaline earth metals. Under terrestrial conditions, hydrated sulfate minerals are common in various geological environments. Whereas the anhydrous sulfate minerals of alkali, alkaline earth and transition metals formalmost exclusively in active fumaroles.The fumaroles of Tolbachik volcano are a unique mineralogical locality with a large number of endemic mineral species. The variety of sulfate minerals observed in Tolbachik fumaroles is impressive. Since 2014, we have discovered 11 new mineral species with sulfate anions of fumarolic origin. Many of the fumarolic minerals demonstrate unique structure types with unprecedented and complex architectures and have no synthetic analogues. Several examples of the recently obtained synthetic sulfate materials inspired by Nature will be discussed.