Cloaking, based on transformation optics, describes the process of shielding something from view by controlling electromagnetic radiation. Objects in the defined location are still present, but incident waves are guided around them without being affected by the object itself. In this report, we review the theories and experiments behind the cloaking concept and suggest what devices might realistically be expected in the near future and what is likely to prove impossible. The analysis shows that the permittivity and permeability of an invisibility cloak must be highly anisotropic (directionally dependent) and inhomogeneous (composed of different materials). By manufacturing composite materials that mimic these properties cloaking has been demonstrated for microwaves in 2D. The resonant structures that constitute the shell limit the bandwidth of operation. There remain challenges for implementations in 3D. However, one can sweep things under the carpet without resorting to resonant structures. So-called carpet cloaks that make rough surfaces look flat have been realized over a broad band of frequencies in the infrared light. Cloaking has been experimentally demonstrated for acoustic wave propagation and thermal conduction in 2D. In the acoustic case, the metamaterial shell has mechanical properties that bend sound around an object under water. The Swedish Armed Forces may be interested in developing this technology to hide submarines from sonar, or to create a new class of stealth ships. We also give examples of antimagnets in 3D, consisting of two homogenous and isotropic materials. These structures act as invisibility cloaks for static uniform magnetic fields and can provide significant benefits in reducing the magnetic signature of ships or submarines. The experiments made in recent years show that it is possible to build structures that bend waves and heat around obstacles in 2D. In the future we expect to see 3D demonstrations. The bandwidth will likely be severely limited for wave propagation problems. For static problems and heat conduction there are no such limitations. Finally, as with many grand challenges, it will probably be the case that the technology being developed will have many more applications than cloaking. The ability to design and build a system that exerts detailed control over the flow of energy is a powerful tool that is bound to find many applications, though perhaps not all of quite such a sensational nature as a cloak.