Anisotropy is the dependence of the velocity on direction; dispersion is the dependence of the velocity on frequency [Formula: see text] (or wavelength [Formula: see text]). These apparently disjoint phenomena can be dealt with together if one uses as the common independent variable the wave vector [Formula: see text], a vector in the direction of the wave and normal with length proportional to the wavenumber [Formula: see text]. The phase velocity is [Formula: see text] and the group velocity [Formula: see text], the gradient of [Formula: see text] in [Formula: see text]-space. The most convenient display of anisotropy and dispersion is by surfaces of equal [Formula: see text] (or equal [Formula: see text]), to be determined with the help of a dispersion equation. In isotropic conditions, theseiso-omega surfaces are spheres. If there is no dispersion, the spheres are equidistant. For wave-number regions with dispersion, the spheres have variable spacing. For anisotropic conditions, the iso-omega surfaces are nonspherical but similar and equispaced if the medi-um is nondispersive. If dispersion occurswith anisotropy, the iso-omega surfaces are not equispaced and not necessarily similar. For highlighting the long-wavelength limit of effective-media theories, a different display is advantageous: If one displays the iso-omega surfaces in slowness-vector space [Formula: see text], the iso-omega surfaces collapse into the long-wave slowness surface for the range of validity of the effective-media theory but deviate from the asymptotic slowness surface for frequencies beyond this range. Such displays not only allow quantification of the limits of the theory but also show in which directions and for which frequencies these deviations occur. The application of this concept requires that the dispersion equation be assembled from the solutions of the wave equation in the actual constituent media, not for the replacement medium. For instance, for a layered medium, the wavefield must satisfy the corresponding wave equation in each constituent layer and must be continuous across all interfaces.