Search for neutralino Dark Matter with the AMANDA neutrino telescope and prospects for IceCube

If non-baryonic dark matter exists in the form of neutralinos, a neutrino flux is expected from the decay of neutralino pair annihilation products inside heavy celestial bodies. Data taken with the AMANDA-II neutrino telescope located at the South Pole, have been used in a search for this indirect dark matter signal. Results will be presented from searches for neutralinos accumulated in the Sun, using AMANDA-II data of 2001 and 2003, and in the centre of the Earth, using AMANDA-II data of 2001 to 2003. Future perspectives, achieved by higher statistics data samples acquired during recent years and by the combined AMANDA-IceCube detector, will also be discussed.