Paper folding, or origami in Japanese, is a traditional craft that has been enjoyed by both children and adults for hundreds of years. Mathematicians have long studied the mathematics of paper folding. They use square papers to construct mathematical shapes (for example, folding an equilateral triangle from a square paper or trisecting an angle), demonstrate geometric properties, and pose and prove problems that arise from paper folding. The geometric connections between origami folding and mathematics, such as shapes and symmetries, can easily be observed. This article will examine the mathematics that arises from three paper folding models.