The benchmark research paper on carbon nanotubes (CNTs) in 1991 by Iijima was a major step forward in applicability of nanotechnology and opened up a whole new field of scientific research. Motivated by CNTs, abundant research efforts have been devoted to nanoscale tubular forms of various solids in recent years. Silicon carbide nanotubes (SiC nanotubes), first synthesized in 2001, have attracted much attention because of some expected advantages over CNTs. However, because of limitations of experimental methods, there is still no simple way to prepare them and some of the SiC nanotubes produced have been found to be thermally unstable. Hence, many theoretical methods such as the first principle method and molecular dynamics method are employed to investigate their properties. In the present research, electronic structures of intrinsic and doped single-walled SiC nanotubes (SiCNTs) have been simulated and computed based on the first principles of density functional theory (DFT), which may provide theoretical guidance for applications in novel gas sensors, energy storage and nano-electronic devices. Due to their polar nature, SiCNTs exhibit better reactivity toward many gas adsorbates than CNTs. Here, we have reported SiCNTs as a novel sensor for formaldehyde (HCOH), a major indoor air pollutant known to be the cause of many diseases. Compared with the weak adsorption on CNTs, HCOH molecule tends to be chemisorbed to the Si-C bond of SiCNT with appreciable adsorption energy. The electronic structure of SiCNT undergoes a remarkable change caused by the adsorption of HCOH molecule. And with the increase of the coverage of the adsorbed HCOH molecules, the band gap of SiCNT decreases gradually, leading to an enhancement of the conductivity of SiCNTs and indicating that SiCNTs have high sensitivity to HCOH gas. The adsorption of hydrogen molecules (H2) on the perfect and lithium (Li) doped SiCNTs was also investigated. The high reactivity of exterior surface makes SiCNT easily interact with H2 with binding energy of about 0.080 meV, much larger than that with CNTs. However, to be ideal hydrogen storage materials, the binding energy of hydrogen molecules should be in the range of 0.2-0.6 eV/H2 as specified by the U.S. Department of Energy. Thus hydrogen molecules can be adsorbed and desorbed at room temperature and ambient pressure. Hence, in our work, Li atom is used to decorate SiCNT. Both structures of Li adsorbed on the exterior of SiCNT and Li encapsulated in the SiCNT are considered. The electronic structure has a significant change when Li atom is adsorbed on the exterior of SiCNT and new states close to the Fermi level is introduced. For Li-encapsulated SiCNT, the charge transferred from the Li atom to the nanotube is 0.15 electrons and remains located near the Li atom. The binding energy between H2 and Li-adsorbed SiCNT rises to 0.211 eV due to the large charge transfer from Li to the nanotube, while H2 interacting with Li-encapsulated SiCNT has almost the same binding energy with that of pristine SiCNT. Up to four H2 molecules can be attached to Li-adsorbed SiCNT with an average binding energy of 0.165 eV, which is close to the lowest requirement proposed by the U.S. Department of Energy, indicating that this system is a good storage medium for H2. Although the doping of Li increases the binding energy of H2 and SiCNT, the interaction between Li atom and SiCNT is weaker than the cohesive energy of bulk lithium. Hence, to enhance the exterior activity of SiCNTs, Stone-Wales (SW) defective SiCNTs are taken into account. Using DFT, it is found that the defects in SiCNTs increase the binding energies with Li atom and narrow the HOMO-LUMO gaps of the adsorbed systems. Many different stable configurations that occur after adsorption are investigated and it implies that fine tuning of the reactivity of the adsorbed Li atom can be achieved through introducing defect sites. Furthermore, the structures and electronic states of Li+ interaction with pristine and SW defective SiCNTs have also been studied to investigate the potential application of SiC nanostructures in Li ion batteries. This shows Li+ also prefers to interact with defective-SiCNTs and the lithium always remains positively charged. The investigation of the diffusion-barrier for the perfect SiCNT and SiCNT with topological defects shows that insertion of lithium ions through the side-wall of SiCNT seems energetically unfavorable, like CNTs, unless there are structural defects. The barrier height decreases from 10.4 to 2.5 eV as the ring size of the wall increases from pentagon to heptagon. It has been indicated that SiCNTs are always wide-band semiconductors with the band gap highly dependent upon their diameter rather than helicity. Zig-zag SiCNTs are direct band gap semiconductors, whereas armchair and chiral tubes are indirect band gap semiconductors. To modify electronic properties of SiCNTs to satisfy the requirements for actual applications, fluorination is applied in our work. It is found that F atoms prefer to adsorb on Si sites of both zig-zag (8,0) and armchair (6,6) SiCNT with remarkable binding energy due to the ionic-covalent resonance bond of Si-C. The electronic states of SiCNT significantly change because of F doping. A push down of the Fermi level for both types of SiCNTs is observed after the chemisorption of F atom on Si site, whereas the Fermi levels are lifted up when F atom is attached on the C site of the tubes. Fluorine adsorption in case of either a single silicon or single carbon atom yields spontaneous magnetization and the net magnetic moment is 1μB. Increase in the diameter of SiCNTs results in the monotonically decreased magnetic moment due to exchange splitting of the defect band near the Fermi level. It is expected fluorination may lead to a new approach to tuning of the electronic and magnetic properties of SiCNTs toward some nanoelectronics and metal-free magnetic materials.