A dual equivalence for an arbitrary collection of combinatorial objects endowed with a descent set is a relation for which equivalence classes group together terms according to the Schur expansion of the corresponding generating function. After outlining the definition of dual equivalence, we'll present three main applications: the Schur expansion of Macdonald polynomials, Schur positivity of k-Schur functions (joint with S. Billey), and a combinatorial rule for the Littlewood-Richardson coefficients of the Grassmannian in the special case of a Schubert polynomial times a Schur function (joint with N. Bergeron and F. Sottile).