We describe several corollaries of the Littlewood-Richardson refinements, including a method for multiplying two Schur functions with different numbers of variables and expanding the result as a sum of key polynomials. We use interactions between Schur functions and quasisymmetric Schur functions to prove a conjecture of Bergeron and Reutenauer. We show that their conjectured basis is indeed a basis for the quotient ring of quasisymmetric functions by symmetric functions, which also provides a combinatorial proof of Garsia and Wallach's results about the freeness and dimension of QSym/Sym. This is joint work with Aaron Lauve.