In many science areas, the quest for increased computational resources is driven by a need to span a broader range of scales, that is, to capture the interaction of small scales with the large. In transport problems such as electromagnetics and fluid mechanics, this implies a need to propagate small scale features over long times and distances. In numerical simulations, such long-time integrations are most efficiently realized by using high-order discretizations. Here, we present recent advances in spectral element methods designed for the petascale efficient single- and multi-node performance. Application areas include the study of magnetorotational turbulence in accretion disk models, heat transfer in advanced reactor designs, wakefield computations in accelerators, and transition to turbulence in vascular flows.