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).