Magnetism is very important in various areas of science and technology, ranging from magnetic recording through energy generation to trapping cold atoms. Physicists have managed to master magnetism-to create and manipulate magnetic fields-almost at will. Surprisingly, there is at least one property that has been elusive until now: how to 'switch off' the magnetic interaction of a magnetic material with existing magnetic fields without modifying them. Here we introduce the antimagnet, a design that conceals the magnetic response of a given volume from its exterior, without altering the external magnetic fields, in some respects analogous to recent theoretical proposals for cloaking electromagnetic waves with metamaterials. However, unlike these devices, which require extreme material properties, our device is feasible and needs only two kinds of available materials: superconductors and isotropic magnetic materials. Antimagnets may have applications in magneticbased medical techniques such as magnetic resonance imaging or in reducing the magnetic signature of vessels or planes. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.