We explore the capabilities of the upcoming Deep Underground Neutrino Experiment (DUNE) to measure ${\nu }_{\tau }$ charged-current interactions and the associated oscillation probability $P({\nu }_{\mu }\to {\nu }_{\tau })$ at its far detector, concentrating on how such results can be used to probe neutrino properties and interactions. DUNE has the potential to identify significantly more ${\nu }_{\tau }$ events than all existing experiments and can use this data sample to nontrivially test the three-massive-neutrinos paradigm by providing complementary measurements to those from the ${\nu }_e$-appearance and ${\nu }_{\mu }$-disappearance channels. We further discuss the sensitivity of the ${\nu }_{\tau }$-appearance channel to several hypotheses for the physics that may lurk beyond the three-massive-neutrinos paradigm: a nonunitary lepton mixing matrix, the $3+1$ light neutrinos hypothesis, and the existence of nonstandard neutral-current neutrino interactions. Throughout, we also consider the relative benefits of the proposed high-energy tune of the Long-Baseline Neutrino Facility (LBNF) beam line.