  Let K be a non-archimedean field with residue field k, and suppose that k is
not an algebraic extension of a finite field. We prove two results concerning
wandering domains of rational functions f in K(z) and Rivera-Letelier's notion
of nontrivial reduction. First, if f has nontrivial reduction, then assuming
some simple hypotheses, we show that the Fatou set of f has wandering
components by any of the usual definitions of such components. Second, we show
that if k has characteristic zero and K is discretely valued, then the converse
holds; that is, the existence of a wandering domain implies that some iterate
has nontrivial reduction in some coordinate.
