Cosmological measurements have revealed that matter familiar to us makes up only approximately 5% of the energy density of our universe. The remainder has been labelled Dark Matter (about 26%) and Dark Energy (the rest). This paper summarises how the IceCube Neutrino Observatory situated at the South Pole is being used to search for direct evidence of Dark Matter. Supersymmetry (SUSY) models are regarded as the most promising extensions of the Standard Model, and the paper describes the tests of SUSY predictions for the annihilation of Dark Matter in the core of the sun. The lack of an observable signal is used to constrain the set of values for free parameters within the SUSY model. IceCube's results complement those from other experiments which use different detectors for Dark Matter interactions, and together are placing meaningful constraints upon the most promising SUSY models.