As the low-energy infill array of the IceCube Neutrino Observatory at the South Pole, DeepCore allows performing high statistics studies of atmospheric neutrinos with energies down to around $5\,\mathrm{GeV}$. This low energy threshold enables DeepCore to resolve characteristic distortions of the atmospheric neutrinos' energy and zenith angle distributions. Based on a set of neutrinos collected over three years of operation, the atmospheric oscillation parameters $\theta_{23}$ and $\Delta m^2_{32}$ are measured with a precision competitive with long-baseline experiments. With a further reduction of the in-ice energy threshold and improved reconstruction resolutions, the "IceCube Upgrade" will focus on dedicated oscillation measurements that are unique to the flux of atmospheric neutrinos. At the same time, the upgrade will serve as a stepping stone toward the physics goals of PINGU---an envisaged, even more densely instrumented array dedicated to determining the neutrino mass ordering.