Though the introduction of optical invisibility cloaks in 2006 caused a huge sensation around the world in both the media and the general public, arguably even more significant to the optical science community is the technique used to design cloaks.
The original cloaking papers took advantage of the observation that a physical warping of space can be simulated by an appropriately-designed material medium. To design a cloak, we first figure out how we want to bend space around a cloaked region, and then it is relatively straightforward to figure out the medium that simulates that bent space.
How does this work? Let us imagine that we have an ordinary, unbent, region of space. To design an invisibility cloak, we imagine poking a pointlike hole in that space and stretching it to make a void. Physically, that void is completely inaccessible — it lies outside of ordinary space. This is illustrated below. Ordinary space is on the left, with a ray of light and the point that gets stretched into a void on the right. The ray gets bent away from the void thanks to the distortion of space.