We will address the representation theory of Galois algebras, family of associative algebras which have certain invariant skew group ring structure. Examples include generalized Weyl algebras, universal enveloping algebras of sl(n), finite W-algebras of type A etc. We will focus on the combinatorics of their Gelfand-Tsetlin representations based on recent joint results with D.Grantcharov, L.E.Ramirez, P.Zadunaisky and J.Zhang.