Discover has this great article about really fine-tuned origami work. Your typical origami design usually has single digit number of folds, rarely getting close to two dozen. Folks like Robert Lang use special software (written by Lang) to help them analyze the ways to fo ld a single square of origami paper to come up with amazingly detailed origami sculptures. There are also folks like Satoshi Kamiya who create these masterpieces without the aid of software.
Here are examples of Lang’s work (a seven inch walking insect) and Kamiya’s work (a dragon).