The 40kt DUNE Far Detector, located at the Sanford Underground Research Facility, will offer unique capabilities for the study of atmospheric neutrinos. Due to the detector's excellent energy resolutions, angular resolutions, and particle ID capabilities, atmospheric neutrino analyses in DUNE can provide valuable information about 3-flavor oscillations, despite the relatively modest statistics. These data provide a complementary analysis approach to beam neutrinos, and can help resolve ambiguities in beam-only analyses. In this paper we show the prospects on the determination of the mass hierarchy, octant of $\theta_{23}$, and measurement of $\delta_{CP}$ using atmospheric neutrinos in DUNE. Atmospheric neutrinos can also lead to a variety of beyond the standard model scenarios for neutrino transitions, propagation, and interactions. Examples that have been previously studied include CPT violation, Lorentz invariance violation, non-standard interactions, mass varying neutrinos and sterile neutrinos.