  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 non-unitary lepton mixing matrix, the
$3+1$ light neutrinos hypothesis, and the existence of non-standard
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.
