For typical magnetic materials, as the temperature decreases long range magnetic order occurs at a finite temperature, consistent with the Third Law which requires that the entropy (in this case spin disorder entropy) should approach zero as T approaches zero. In contrast for geometrically frustrated magnets in which the spins are arrayed on triangular or tetrahedral lattices, the long range ordered state is often unstable with respect to more exotic ground states such as spin glasses, spin ices and spin liquids. Following a brief introduction and review of geometric frustration, recent experimental results based on a series of materials known as ordered double perovskites (in which the magnetic lattice is face-centred cubic) will be reviewed with attention to the observation of unusual ground states. The roles of spin and orbital degrees of freedom will be emphasized. There will be an attempt to connect these results with the limited theory on this class of materials.