The IceCube observatory located at the South Pole is a cubic-kilometre optical Cherenkov telescope primarily designed for the detection of high-energy astrophysical neutrinos. IceCube became fully operational in 2010 and reached a milestone in 2013 by the first observation of cosmic neutrinos in the TeV-PeV energy range. This observation does not only mark an important breakthrough in neutrino astronomy, but it also provides a new probe of particle physics related to neutrino production, mixing, and interaction. An overview is given of the various possibilities how IceCube can address fundamental questions related to the phenomena of neutrino oscillations and interactions, the origin of dark matter, and the existence of exotic relic particles, like monopoles. Recent results are summarized and future avenues are highlighted.