In this paper, we have reviewed some of the recent theoretical studies on the electronic and structural properties of silicon nanotubes from single-walled to double-walled nanostructures, primarily focusing on the studies performed by the present authors. The studies so far have not indicated any metallic behavior in both single-walled and double-walled silicon nanotubes. Atomic and molecular adsorptions of elements including hydrogen, oxygen and alkali metals on single-walled silicon nanotubes are also reviewed and new results presented in detail. A systematic study of molecular adsorption and co-adsorptions of hydrogen and oxygen molecules in zigzag silicon nanotube (SiNT) has been performed using hybrid density functional theory. For adsorption of two hydrogen molecules in SiNT (10, 0), the original diatomic molecular structure was maintained after adsorption. The most preferred final site for hydrogen molecules is the on-top site. For adsorption of two oxygen molecules, the most preferred sites are bridge sites, which are the parallel or zigzag bridge sites. Complete dissociation, partial dissociation and non-dissociation were observed for adsorption of two oxygen molecules. Peroxide structure and Si-O-O structures have also been observed in adsorption of two oxygen molecules with smaller adsorption energies rather than complete dissociation. For the co-adsorption of one hydrogen molecule and one oxygen molecule, the hydrogen molecule is slightly polarized, and a suppression effect on HOMO-LUMO gap was observed.