Check out Susan Orlean's fascinating New Yorker profile of origami artist Robert J. Lang in the current edition. This origami is way beyond the simple cranes and goldfish of your childhood.
Lang is a physicist who developed an intense interest in origami as a child. He has since used his math and science skills to develop computer software that enables him to fold incredibly complex creatures and objects. The level of detail is astounding (look for the fish that comes complete with scales on his web site). As he says in the article, the software allows him to pretty much make any creature he wants, even people.
And he does it all with only one sheet of paper per creation.
And it isn't all just fun. Lang puts his skills to work in areas of medicine and industrial design, finding ways to fold a heart implant so it could be inserted through a small tube but unfold to encompass the heart. He was also contracted to figure out how to fold a telescope so it could be transported into space.
I wanted to post images of his creations (the one element missing from the New Yorker profile) but Lang is understandably restrictive about copyrighting his work, so you'll have to check out his web site to see his astonishing work.