Carbon nanotubes are nanometer sized cylinders made of carbon atoms which possess extraordinary electrical, thermal and mechanical properties. Their potential applications include diverse areas such as conductive and high strength composites, energy storage and conversion devices, sensors, field emission displays and radiation sources, hydrogen storage media, semiconductor devices, probes and interconnects. A single-walled carbon nanotube is formed from a single atomic layer comprised of a hexagonal network of carbon atoms and it is of interest to understand how the underlying atomic structure determines its macroscopic properties. In describing such atomic systems, all-atom simulations are often employed, but are limited by computational expense. Alternatively, continuum models are efficient, but the traditional ones suffer from inaccuracies due to surface, interface, size effects and ambiguities in model parameters. This book focuses on coupled atomistic-continuum models which combine the advantages of modeling at either scale. They account for anisotropic and large- strain effects using ideas that can be extended to other atomic systems.