Seiberg-Witten theory has an analogue for 3- and 4-manifolds with involutions called real Seiberg-Witten theory. This theory can be used to construct invariants of links and embedded surfaces by passing to double branched covers. This talk will focus on a framed version of real Seiberg-Witten-Floer homology. It turns out this invariant of links has rather surprising properties not seen in ordinary Seiberg-Witten theory. I will explain why it is special and how it is related to some recent developments.