The 1-, 2-, and 3-dimensional structures obtained from conjugated rings of carbon atoms are reviewed. They include finite small and large molecules (benzenoids, collarenes, beltenes, cyclacenes, cyclophenacenes, Möbius analogs, nanotori) and infinite macromolecules, nets and tilings (graphene, defected graphene, fractal benzenoids, nano-tubes, nano-cones, etc.). A few challenges for future expe...