We present atmospheric and astrophysical neutrino oscillation results from IceCube. Starting with IceCube's DeepCore detector, we show measurements that are highly competitive with dedicated neutrino oscillation experiments but in a different energy regime and with different systematics. We discuss IceCube's recently deployed sensors (the "Upgrade") which will further enhance our sensitivity to atmospheric neutrino oscillations, including atmospheric muon neutrino disappearance, tau neutrino appearance, and the neutrino mass ordering. Using higher-energy data from the full IceCube array, we present the discovery of astrophysical tau neutrinos, confirming that neutrinos oscillate at ultra-high energies over ultra-long baselines, while also providing the first constraints on the nature of their astrophysical sources.