Deep Underground Neutrino Experiment, which is being actively developed by an international collaboration of 1,000+ researchers from 30+ countries, will be a multi-decade physics program. The experiment will carry out precision oscillation measurements in the neutrino beam created at Fermilab, look for nucleon decay, and be ready to capture a burst of neutrinos from a galactic core-collapse supernova. Theoretical input is essential for many aspects of this program. In the first part of the talk, I will discuss some relevant aspects of the neutrino-nucleus cross section physics and related questions about measuring neutrino energy at DUNE. In the second part, I will focus on the astrophysical capabilities of the far detector. I will show that the supernova burst signal carries in it the signatures of physical processes taking place close to the collapsed core. If we know what to look for, we can learn about the conditions in the neutrino-driven wind and the impact of collective flavor oscillations.