The last few invisibility cloaks we've seen have relied on metamaterials to make tiny objects invisible to a specific wavelength of light. This "carpet cloak," from MIT, uses some calcite crystals to make much larger objects disappear in the visible spectrum.
The picture above basically tells the whole story: two calcite crystal prisms are glued together in such a way that a little wedge of space is created underneath. When an object, in this case a roll of pink paper, is placed inside the wedge, it vanishes. The whole point of this cloak is that the object isn't simply covered up; when you look at the crystal, it appears as though it's completely empty with a visible and flat bottom surface.
The current incarnation of the calcite cloak was built for a mere $1,000 out of natural calcite crystals, and can hide objects with a maximum height of 2mm. However, there's no reason why the crystals couldn't be scaled up to hide larger objects, and using artificial crystals might keep the cost down at the same time, although hiding yourself under a couple giant blocks of calcite might not be the most effective way of not being seen. Even so, the MIT researchers are already thinking ahead about the potential applications for their cloaking technology:
"A fully functional invisibility cloak can have important applications especially in areas of defense and security. The cloak can also be used to hide cables on the seabed or help biologists in marine research where fish or other ocean creatures are not disturbed."
Yep, never mind about super powers and saving the world and stuff, let's just focus on not freaking out fish.