Spatial attenuation of sea waves can be caused by radiation of incoherently scattered waves, in addition to bottom friction. We describe recent theories of water waves scattered by a long stretch of randomly rough seabed, where the root-mean-square height of the roughness is moderately small compared to the sea depth. Two separate theories will be reported for wavelength comparable to and much smaller than the water depth. By using two-scale expansions and Green’s functions, evolution equations for the wave amplitudes are derived. In finite depth, narrow-banded, nearly monochromatic waves are found to be governed by a nonlinear Schr¨odinger equation, modified by an additional complex damping term. For periodic waves in shallow water, energy exchange among different harmonics is accompanied by radiation damping. For a transient wave pulse in shallow water, disorder gives rise to a diffusion equation with additional terms representing effects on phase velocity and dispersion. A variety of numerical examples will be discussed.