A new pressure-measurement technique which employs the tools of molecular spectroscopy has recently received considerable attention in the fluid mechanics community. Measurements are made via oxygen-sensitive molecules attached to the surface of interest as a coating, or paint. The pressure-sensitive-paint (PSP) technique is now commonly used in stationary wind-tunnel tests; this thesis presents the extension of the technique to advanced turbomachinery applications. New pressure- and temperature-sensitive paints (TSPs) have been developed for application to a state-of-the-art transonic compressor where pressures up to 2 atm and surface temperatures up to 140° C are expected for the first-stage rotor. PSP and TSP data has been acquired from the suction surface of the first-stage rotor of a transonic compressor operating at its peak-efficiency condition. The shock structure is clearly visible in the pressure image, and visual comparison to the corresponding computational fluid dynamics (CFD) prediction shows qualitative agreement to the PSP data.