We investigate some aspects of the physics of wave propagation at the ocean bottom (ranging from soft sediments to crustal rocks). Most of the phenomena are associated to the presence of attenuation. The analysis requires the use of an anelastic stress-strain relation and a highly accurate modeling algorithm. Special attention is given to modeling the boundary conditions at the ocean-bottom interface and the related physical phenomena. For this purpose, we further develop and test the pseudospectral modeling algorithm for wave propagation at fluid-anelastic solid interfaces. The method is based on a domain-decomposition technique (one grid for the fluid part and another grid for the solid part) and the Fourier and Chebyshev differential operators. We consider the reflection, transmission, and propagation of seismic waves at the ocean bottom, modeled as a plane boundary separating an acoustic medium (ocean) and a viscoelastic solid (sediment). The main physical phenomena associated with this interface are illustrated, namely, amplitude variations with offset, the Rayleigh window, and the propagation of Scholte and leaky Rayleigh waves. Modeling anelasticity is essential to describe these effects, in particular, amplitude variations near and beyond the critical angle, the Rayleigh window, and the dissipation of the fundamental interface mode. The physics of wave propagation is investigated by means of a plane-wave analysis and the novel modeling algorithm. A wavenumber–frequency domain method is used to compute the reflection coefficient and phase angle from the synthetic seismograms. This method serves to verify the algorithm, which is shown to model with high accuracy the Rayleigh-window phenomenon and the propagation of interface waves. The modeling is further verified by comparisons with the analytical solution for a fluid-solid interface in lossless media, with source and receivers away from and at the ocean bottom. Using the pseudospectral modeling code, which allows general material variability, a complete and accurate characterization of the seismic response of the ocean bottom can be obtained. An example illustrates the effects of attenuation on the propagation of dispersive Scholte waves at the bottom of the North Sea.