  After a brief discussion of the structural trends which appear with
increasing number of atoms in B cages, a one-to one correspondence between the
connectivity of B cages and C cage structures will be proposed. The electronic
level spectra of both systems from Hartree-Fock calculations is given and
discussed. The relation of curvature introduced into an originally planar
graphitic fragment to pentagonal 'defects' such as are present in
buckminsterfullerene is also briefly treated.
  A study of the structure and electronic properties of B nanotubes will then
be introduced. We start by presenting a solution of the free-electron network
approach for a 'model boron' planar lattice with local coordination number 6.
In particular the dispersion relation E(k) for the pi-electron bands, together
with the corresponding electronic Density Of States (DOS), will be exhibited.
This is then used within the zone folding scheme to obtain information about
the electronic DOS of different nanotubes obtained by folding this model boron
sheet.
  To obtain the self-consistent potential in which the valence electrons move
in a nanotube, 'the March model' in its original form was invoked and results
are reported for a carbon nanotube.
  Finally, heterostructures, such as BN cages and fluorinated
buckminsterfullerene, will be briefly treated, the new feature here being
electronegativity difference.
