Origami is the ancient Japanese practice of paper folding, where cuts are not allowed, to make intricate works of art that are sometimes minimalist and sometimes amazingly complex and realistic. The past 5-10 years have seen a surge of interest in origami for applications in engineering, physics, architecture, and other branches of science. Origami is being used to design solar sails that unfold without the aid of human hands in outer space. It is being used to design innovative heart stents, automobile airbags, and even micro-scale robots. Materials scientists are finding ways to fold everything from graphene to polymer gels to sheet metal. This presentation will describe how origami is being used in science, how mathematics has unlocked the power of origami to make it useful in such applications, and how origami is being used in education as a hands-on way to teach math.