Thomas Streicher has reformulated Krivine's notion of classical realizability into abstract Krivine structures and showed that from any such structure one can build a tripos out of it. They are called Krivine triposes and form a subclass of relative realizability triposes in the sense of van Oosten and Hofstra. In this talk, I will present a characterization of those Krivine triposes, indeed, they are exactly boolean subtriposes of relative realizability triposes. I will also talk about a concrete construction of non-localic Krivine triposes. These results are from my master thesis supervised by Jaap van Oosten.