  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, after a
seven-year construction phase, 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. In this review we give an overview 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. We will summarize
recent results and highlight future avenues.
