Highly sensitive magneto-optical techniques have been used to investigate weak linear and nonlinear optical absorption mechanisms in p- and n-type InSb. As a result, new absorption processes involving both impurities and free carriers have been identified and studied in detail. For p-InSb, magneto-optical spectra has been obtained over a wide range of temperatures and photon energies. The spectra obtained at higher sample temperatures are seen to result from combined-resonance transitions of free holes between heavy-and light-hole Landau levels, while bound-hole transitions between ground heavy-hole-like and excited light-hole-like acceptor states are observed at lower temperatures. Analysis of the combined-resonance data along with extensive intra-conduction band and two-photon interband data using a modified Pidgeon and Brown 8X8 energy band model has allowed the determination of a single set of band parameters for InSb that quantitatively describes these different sets of data. In addition, a ground state binding energy of 8.1 meV for Cd acceptors and 42.5 meV for Au acceptors has been extracted from the analysis of the bound-hole spectra. For n-lnSb, photo-Hall techniques have been developed and used to study both resonant impurity and two-photon magneto-absorption (TPMA) processes in detail. As a result, LO-phonon-assisted impurity cyclotron resonance harmonic (LOICRH) transitions from …