Stable Schubert polynomials (aka Stanley symmetric functions) are Schur-positive symmetric functions, whose Schur coefficients can be described either by a recurrence coming from Monk's rule, or combinatorially by the Edelman-Greene insertion algorithm. We give analogous results for what we call involution Schubert polynomials---representatives for the cohomology classes of the closures of the O(n)- or Sp(2n)-orbits on the complete flag variety, first described by Brion and Wyser-Yong---where now Schur-positivity is replaced by Schur-P-positivity. A new Littlewood-Richardson rule for Schur P-functions follows as a special case. We also give a new proof of results of DeWitt and Ardila-Serrano classifying skew Schur functions which are Schur-P-positive. This is joint work with Zach Hamaker and Eric Marberg. Speaker(s): Brendan Pawlowski (University of Michigan)