When the people of the Greek city of Delos asked the Delphic oracle how to stop a plague that Apollo sent to them, the oracle answered that they should duplicate the cubic altar of this god. Although the efforts of the great mathematicians of the day, none of them was able to double the cube through straightedge and compass (as the fashion of the day requested in geometry). As we know nowadays, this latter task is impossible; however, if we allow ourselves to use origami, the duplication of the cube and other classical geometric problems not solvable by straightedge and compass can be solved. In the talk, we will explore the constructions that the use of origami permits in classical geometry.