Phil mentioned Ireland’s Mcor Technologies when they premiered on Gizmodo back in 2008. Their monochrome Matrix 300+ printer, shown off in the above video, builds models by laminating regular copy/printer paper using controlled application of adhesive and 2D-mechanical cutting on each layer. A complete description is available in US Patent Application 2011/0094441.
Now, Mcor is at work on Iris, a prototype design that implements a full-color version of their process, presumably adding a color printing step, of some sort, on each sheet of paper. Check the video below to see some early results.