The invisibility cloak appears to have the shape of a "true cloak" or more like a "poncho shape". It's thickness/thinness is explained by the researchers as being made of a homogeneous construction of resistors. The secret/s of its invisibility property is said to be due to permittivity and permeability. It is not known which wavelengths or frequencies in which it is "invisible". For a "non-action video" - that may have technical issues - one was developed by TechNetworkNews. You may have to look into the ALP* article for a demonstration, if possible.
The "prior art" of the invisibility cloak was being developed on the basis of metamaterials. However that last link (from the Wikipedia) is current up to only 2010. But the prior art does date back to 2005/2006. For a good working development (based on nanomaterials) see the YouTube video from/by Ali Aliev. For more on that development see our Examiner.com article. If you read the article you should see that that invisibility device - as is - might be impractical for your room temperature full optical wavelength invisibility cloak. But, it is apparently invisible in the optical range of light visible to human eyes.
For more on the recent (November 2012) invisibility cloak/device from Duke University see our other Examiner.com article. Like some invisibility devices it does not cover the optical range and works only in the microwave range. However, it does give a working demonstration that the next advance to the optical range cloak could be possible.
The prior art to that work was the research and development of metamaterials (earlier, more) for "fishnet" invisibility cloaking - a design which was in favor. See the articles "Low-loss negative-index metamaterial at telecommunication wavelengths" and "Development of bulk optical negative index fishnet metamaterials: Achieving a Low Loss and Broadband Response Through Coupling". The thinking at the time was the development of a "layered, pierced metamaterial" with a negative refractive index.
The layers of materials might be nano-scale coatings of silver sandwiching a dielectric (like Magnesium fluoride). The advantage/s of silver being it's high reflectivity and "damping" properties. Magnesium fluoride was seen to have an advantage in its relative clarity, we surmise. Other dielectrics might be worth reviewing at a later time. A superconductor might also replace silver due to it's high permeability. However, superconductors (at this writing) have disadvantages like a very low operating temperature and lack of optical clarity. Would elemental Niobium work in this case? We can't say.
Silicon - combined with metallics - was also a research topic in 2009. However, the cloak developed by the Berkeley Lab was said to be invisible only in the near infrared wavelength - slightly outside the range of human optical visibility. However, it too, was something of a "fishnet" material. (See also the video at top of the post.)