The first and second moments, i.e., the coherent field and the two‐point, two‐time correlation function, are calculated for the acoustic fields scattered from various rough surfaces. For each surface they yield the reflection, absorption, and differential scattering coefficients, as well as an equivalent boundary condition for the coherent field. Renormalized coefficients are constructed to eliminate divergences at grazing incidence. The results are specialized to surfaces which are statistically homogeneous in both space and time, and to surfaces consisting of randomly placed bosses on a smooth surface. The surfaces considered are slightly rough, moving, soft or hard boundaries, and flat surfaces with random admittances or impedances. The analysis is based on the regular perturbation method or Born approximation. Comparisons with previous results are made.