Low dimensional systems refer to those systems in which at least one of the three dimensions is intermediate between those characteristic of atoms/molecules and those of the bulk material, generally in the range from 1 nm to 100 nm. Examples of low dimensional systems are 2-dimensional electron gases, nanowires, nanotubes and quantum dots, etc. Those systems can have very high surface area to volume ratio. Consequently, the surface states become important and even dominant. In addition, the dimensional constraint on the system gives rise to quantum size effects, which can significantly change the energy spectrum of electrons and their behavior. As a result, some properties of such systems are very different from those of their bulk counterparts. Those systems have shown a kaleidoscope of intriguing phenomena and extraordinary electronic, optical, thermal, mechanical and chemical properties, which may result in their use in wide range of nanotechnology.