One of the pivotal moments in the history of nanotechnology was the experimental discovery of the Buckminster Fullerene in 1985, for which Smalley, Kroto and Curl recieved the 1996 Nobel Prize in Chemistry. We will tell the story of this amazing discovery and explore the fascinating science of fullerenes and nanotubes which spans many disciplines including chemistry, physics, technology and recreational mathematics. We will also explore means by which fullerenes and nanotubes structures can be constructed in the classroom using beads and strings (a technique known as beaded molecules) or with modular origami.