The motivation for the exciton studies was based on interest in material characterization and study of the band structure of the InSb quantum wells. In this thesis, we have presented spectroscopic studies of InSb quantum wells using FTIR spectroscopy to probe the interband transitions. First we performed exciton measurements on InSb/AlInSb QWs with no external magnetic field. A four-band Kane model, including the strain and the nonparabolicity in our system, is used to reproduce experimental transitions. We have followed an alternate method to determine the deformation potential parameters by exploiting the different strain dependence of the light and heavy hole band edges. We find hydrostatic deformation potential parameter a = -7.4 +/- 0.2 eV and shear deformation potential parameter b = -1.8 +/- 0.1 eV and these values are closely agree with most previously reported values The second half of this thesis investigated optical properties of InSb-AlInSb MQW structures in a normal magnetic field. The study leads to an interpretation of optical transitions in undoped systems with different well widths and different Al composition in the barrier. In the magneto-optical investigations, the magnetoexcitons are clearly observed in the undoped MQWs, but are complicated by the band mixing effect. The field dependence of the spectral minima has been fitted within the Pidgeon and Brown model. In every sample, a reasonable agreement between the calculated and experimental results is achieved for most of the transitions. This enables us to identify most of the transitions by their predicted energy-field dependence. Moreover, it is clear that there is no simple linear relationship between the energy shift of the peaks and the magnetic field.