In this talk, I will introduce the concept of a separable commutative algebra in the setting of tt-geometry and discuss its connection to Mathew’s work on Galois theory. Building on this, I will present several classification results for separable algebras in derived commutative algebra and chromatic homotopy theory. In the final part of the talk I will focus attention to the problem of classifying separable algebras in the category of genuine G-spectra for a finite group G.