Our work on carbon nanotubes covers a very wide range of systems and physical phenomena. In terms of structural properties, carbon nanotubes are one of the most anisotropic materials known: in the axial direction they are exceptionally stiff and strong, while radial deformation and radial sliding are quite easily induced. For a tube of large-enough diameter, the "inflated" state of round cross-section is not the lowest energy state. Instead, the system can collapse into a flat ribbon and thereby capture surface energy of adhesion between the inner faces. In addition, tubes can be functionalized with adatoms or adsorbates that cause substantial changes in their electronic and structural properties.