An equivalence relation is introduced on the nonzero elements of the finite field Fpm to classify constacyclic codes of arbitrary length over Fpm. According to the equivalence classes, all constacyclic codes of length ℓps over Fpm and their duals are characterized, where ℓ is a prime different from p and s is a positive integer. Self-dual cyclic codes of length ℓps over Fpm exist precisely when p is equal to two; in this case, all self-dual cyclic codes of length 2sℓ over F2m are presented.