I will discuss joint work with M. Krishna and W. Kirsch in which we prove that random Schrodinger operators on 3-dimensional Euclidean space with random potentials constructed from independent, identically distributed, random variables and single-site potentials given by delta-functions on the 3-dimensional square slattice, exhibit both dynamical localization and dynamical delocalization with probability one. That is, there are regions in the deterministic spectrum that exhibit dynamical localization, and regions that exhibit delocalization in the form of nontrivial quantum transport, almost surely. These models are the first examples of ergodic, random Schrodinger operators exhibiting both dynamical localization and delocalization in dimension three.