As the switching rates in electronic and optoelectronic devices are pushed to even higher frequencies, it is crucial to probe carrier dynamics in semiconductors on femtosecond timescales. Time resolved spectroscopy is an excellent tool to probe the relaxation dynamics of photoexcited carriers; where after the initial photoexcitation, the nonequilibrium population of electrons and holes relax by a series of scattering processes including carrier-carrier and carrier-phonon scattering. Probing carrier and spin relaxation dynamics in InAs and InSb based narrow-gap semiconductors is crucial to understand the different scattering mechanisms related to the systems. Similar studies in InSb quantum wells are also intriguing, especially for their scientifically unique features (such as small effective mass, large g-factor etc). Our time resolved techniques demonstrated tunability of carrier and spin dynamics which might be important for charge and spin based devices. The samples studied in this work were provided by the groups of Prof. Wessels (Northwestern University) and Prof. Santos (University of Oklahoma). Theoretical calculations were performed by the group of Prof. Stanton (University of Florida). The THz measurements were performed at Wright State University in collaboration with Prof. Jason Deibel. This work has been supported by the National Science Foundation through grants Career Award DMR-0846834, AFOSR Young Investigator Program 06NE231. A portion of this work was performed at the National High Magnetic Field Laboratory (in collaboration with Dr. Stephen McGill), which is supported by National Science Foundation Cooperative Agreement No. DMR-0654118, the State of Florida, and the U.S. Department of Energy. / Ph. D.