The idea of invisibility has fascinated people for millennia and has been an inspiration or ingredient of myths, novels and films, from the Greek legend of Perseus versus Medusa to H.G. Well's Invisible Man and J.K. Rowling's Harry Potter. In 2006 invisibility turned from a subject of fiction into an area of scientific research. The first prototype of an electromagnetic cloaking device was demonstrated that operates in the microwave region of the spectrum. In this lecture I explain the main concepts of cloaking devices and some new ideas for broadband invisibility of visual light.