All kinds of cloaks, all kinds of transformations

We review the foundations of transformation optics (the realization of a certain class of coordinate transformations through appropriate metamaterial design), from the perspective of covariant electromagnetic theory. Whilst reproducing the well-known parameter design for a spatial electromagnetic cloak, the covariant approach allows a greater design flexibility, in that coordinate transformation that explicitly include the time coordinate can be addressed. An example of the latter is the so-called spacetime cloak, in which events are concealed from distant observers through the manipulation of light's speed in both space and time. Covariant approaches have also yielded new insights to acoustics in which it has been shown that the underlying geometry of acoustic waves can be expressed as a (pseudo-)Riemanian metric in 4-dimensional spacetime. The role of the underlying velocity field of the medium is emphasized as a key and novel design parameter. The role of curvature in transformation theory is briefly reviewed. Finally, we speculate on the existance of a transformation formalism that can embrace several areas of physics.