The structure of the wall pressure field beneath supersonic adiabatic turbulent boundary layers is analyzed by means of direct numerical simulations at free-stream Mach number M(infinity) = 2, 3, 4, spanning a relatively large range of Reynolds numbers. The data reported in the paper, which include wall pressure fluctuations intensities, frequency spectra, space-time correlations, and convection velocities, show that when pressure is scaled by the wall shear stress, most statistics well conform to low-speed findings, contradicting the conclusions of previous experimental studies. Genuine compressibility effects are found to provide a small contribution to the magnitude of the wall pressure fluctuations, their influence being limited to the high-frequency end of the spectra, where a systematic increase with the Mach number is observed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3622773