The cardinal-valued dp-rank is a measure of the complexity of types and theories, generalizing weight in stable theories to the NIP context. We will present some recent results (joint work with Alf Dolich) on algebraic and topological tameness properties of definable sets in expansions of ordered Abelian groups in which the dp-rank of the universe is finite. In the particular case of definably complete groups of dp-rank 2, we can characterize definable discrete sets, and somewhat weaker results can be proved in the more general context of finite dp-rank.