Abstract: We discuss some recent work studying singularities in mixed characteristic and the first steps towards applications in birational geometry. We introduce mixed characteristic versions of klt/plt singularities and multiplier/adjoint ideals and prove the analogous properties. The theory relies on Andre's work on the existence of perfectoid big Cohen-Macaulay algebras in a weakly functorial sense. Joint work with Karl Schwede, Kevin Tucker, Joe Waldron, and Jakub Witaszek.