The optical properties of InAs/GaSb heterostructures under applied magnetic fields are studied in experimental and theoretical detail. The InAs/GaSb system is a type-II "crossed-gap" system, where the valence band edge of GaSb lies higher in energy than the conduction band edge of InAs. This leads to a region of energy above the InAs conduction band where conduction and hole states mix. Thin-layer superlattices remain semiconducting due to confinement effects, but thick-layer superlattices experience charge transfer which leads to intrinsic carrier densities approaching 10¹² cm^-2 per layer. Existing multi-band modeling techniques based on the <strong>k·p</strong> formalism are discussed, and a method of solving superlattice band structure (the "momentum-matrix" technique) is presented. The quantizing effects of the superlattice layers and applied magnetic fields are investigated, and the selection rules for optical transitions are derived. Standard cyclotron resonance (CR) is used to study effective masses in InAs/GaSb structures. The heavy hole mass is found to be strongly orientation-dependent, with a mass in the [111] orientation reduced 25% from the [001] mass. The electron mass is found to be roughly isotropic with respect to growth orientation, but shows variation with the InAs width due to quantum confinement effects. CR of InAs/GaSb heterojunctions display hitherto unexplained oscillations in linewidth, intensity, and effective mass. A model is proposed which explains the oscillations, based on the intrinsic nature of the InAs/GaSb system. CR is performed on an InAs/GaSb heterojunction using a free-electron laser, where due to the high intensities (on the order of MW/cm²) the absorption process saturates. This saturation allows for a determination of non-radiative relaxation lifetimes, and through the energy dependence of these lifetimes the magnetophonon effect is observed, allowing a direct measurement of LO-phonon-assisted energy relaxation rates. Coupling is introduced into the standard CR experiment, either by tilting the sample with respect to the magnetic field, or by applying a metal grating to the surface. These coupled CR experiments have striking qualitative results which allow for determination of subband separation energies and coupling matrix elements. Photoconductivity experiments are performed on thin-layer (semiconducting) superlattices, showing optical response at far-infrared wavelengths (5-20 μm). The results are compared with <strong>k·p</strong> calculations. One sample is processed for vertical transport, in which conduction occurs perpendicular to the superlattice layers. Strong optical response from this sample indicates the viability of InAs/GaSb-based far-infrared detectors. The momentum-matrix technique is used to predict optimum parameters for semiconducting superlattices with band gaps in the far-infrared. Semimetallic structures are studied via a multi-band self-consistent model, with results corroborating with and extending previous work. Intrinsic structures under applied magnetic field are modeled theoretically for the first time.