A basic family of examples of group actions in the theory of structured ring spectra arises from the theory of Galois extensions, due to Rognes, such as the extension KO KU. I will review the theory of Galois extensions and explain how Galois descent can be used to provide several computations of Picard groups of structured ring spectra such as TMF and certain higher real K-theories. This is based on joint work with Drew Heard and Vesna Stojanoska.