Georg Friedrich Kaulfuss distinguished the genus in 1824 based on samples of S. cyatheoides acquired by Adelbert von Chamisso in 1821. Chamisso had been serving as the naturalist for a Russian scientific expedition led by Otto von Kotzebue aboard the vessel Rurick. Kaulfuss named the genus after Joseph Sadler (1791–1849), a Hungarian naturalist studied European ferns.
As of December 2019, the Checklist of Ferns and Lycophytes of the World accepted the following species:
The Halemaʻumaʻu crater on Kīlauea is named after S. cyatheoides.