Two-dimensional, compressible, turbulent shear layers are studied in a new wind tunnel facility. Both reacting and non-reacting flows are investigated, with one free stream velocity supersonic and the other subsonic. The combustion experiments are based on the use of low concentrations of hydrogen, nitric oxide and fluorine gases. Side-view Schlieren photographs of these reacting and non-reacting flows appear devoid of the two-dimensional, large-scale structures seen in incompressible flows. Comparison with all-subsonic flows produced in the same facility suggests that this lack of two-dimensional structure is due to the presence of the supersonic high-speed free stream velocity. Travelling shock and expansion waves are observed in the high compressibility flows, evidently created by turbulent structures convecting at supersonic velocities. Such waves are seen only in the low-speed fluid, with apparent convection velocities much higher than those predicted on the basis of isentropic pressure-matching arguments. The measured shear layer growth rates agree with previous results by other experimenters, except for a few cases at low compressibility and low density ratio. The fast chemistry regime is attained in some of the high compressibility flows tested. "Flip" experiments conducted in this regime indicate that the volume fraction of mixed fluid in the layer is substantially reduced as compared to previous incompressible results. These same flip experiments also reveal that compressibility significantly alters the entrainment ratio. Finally, it is observed that the shear layer growth rate is relatively insensitive to incident shock /expansion waves and significant heat release inside the shear layer.