"I shall give a brief review of some results on so-called 'electromagnetic cloaking' that have recently received quite a lot of 'popular' attention (for example BBC, CNN and N.Y. Times each had some coverage of associated work in the 'applied physics community' this past summer). Roughly speaking: a cloak is an 'invisible dielectric shield' that makes a designated region in space 'inaccessible' to electromagnetic inspection. In particular I will focus on some quite elementary mathematical 'mapping' techniques,that have extremely interesting implications when it comes to the construction of cloaked, or nearly cloaked regions in space. This talk is intended for a large audience, but for a deeper appreciation of the presentation some knowledge of Partial Differential Equations is a definite plus."