In this talk, I will discuss several positivity phenomena for double Schubert polynomials and explain how they follow from a refined version of Graham’s positivity theorem. These include the monomial positivity of Schubert polynomials, the positivity of the localization formula, the positivity of equivariant Schubert constants, and the positivity of triple Schubert constants. The last result, known as Samuel’s conjecture, implies Kirillov’s conjecture on the positivity of skew divided difference operators applied to Schubert polynomials. I will also present some combinatorial motivations that were not included in our paper. This is joint work with Yibo Gao.