Aspects of extremal surfaces and entanglement entropy in gauge/gravity dualities

I'll briefly review the Ryu-Takayanagi prescription for entanglement entropy in theories with gravity duals, in terms of the areas of certain bulk extremal surfaces. Then I'll discuss gauge/string realizations of some classes of nonrelativistic generalizations of gauge/gravity duality and aspects of entanglement entropy in this context. Finally I'll close with ongoing work on generalizations of these ideas to gauge/gravity dualities involving de Sitter space.