Origami from "ori" meaning "folding" and from "kami" meaning "paper" is the traditional Japanese art of paper folding which started in the 17th century AD and was then popularise outside Japan in the mid 1900s. It has since then evolved into a modern art form. The goal of this art is to transform a flat sheet of material into a finished sculpture through folding and sculpting techniques, and as such the use of cuts or glue are not considered to be origami.
There is much speculation as to the origin of origami. While Japan seems to have had the most extensive tradition, there is evidence of an independent tradition of paperfolding in China, as well as in Germany and Spain. In China traditional funerals included burning folded paper, most often representations of gold nuggets. It is not known exactly when this tradition started but it seems to have become popular during the Sung dynasty (905-11255 CE). The earliest evidence of paperfolding in Europe is a picture of a small paper boat in Tractatus from 1490.
In the early 1900s Akira Yoshizawa was responsible for a number of innovations such as wet folding and his work inspired a renaissance of the art form. During the 1980s a number of fo9lders started systematically studying the mathematical properties of folded forms which led to a steady increase in the complexity of origami models, which continued well into the 1990s, after which some designers started turning to simpler forms.
Here are some great examples of origami that I have found from some fellow Australians: