Ultrafast optical spectroscopy enables us to measure the dynamics of photoexcited free carriers and excitons on the time scale of hundreds of femtoseconds. In low dimensional semiconductor nanostructures such as quantum wire and quantum dot, novel many-body effects involved with Coulomb interaction, exchange and correlation effect are of fundamental interest. In addition, the strong coupling of light to excitons produces a nonlocal dielectric response of the crystal, the spatial dispersion being mediated by the polariton. The optical nonlinearities of exciton-polariton has a great potential in optoelectronic devices, and coherent manipulation of the excitonic quantum state is a building block of quantum information & computation technology.