Nanostructures have interesting properties due to the confinement of electrons in small structures. In addition, since an appreciable fraction of the electronic wave-function resides outside the physical extension of the nanostructure, proximity effects become more important with decreasing size. Moreover, in magnetic nanostructures the magnetic fields also extend a considerable distance outside the physical extent of the nanostructure. Thus, the interplay between size confinement and proximity effects become particularly interesting in magnetic nanostructures. We give two interesting experimental examples of proximity effects with magnetic nanostructures. In one, small magnetic dots radically modify the magnetotransport properties of superconducting films. In the other, the properties of a ferromagnet with nanoscopic antidots are considerably changed because of proximity with an antiferromagnet.