Physically meaningful characterization of seismic-wave attenuation is critical in theoretical and observational seismology. However, currently, descriptions of “attenuation” are somewhat mystified by reliance on empirical concepts, such as time-delayed strain-stress responses and frequency-dependent material properties. Attenuation is often treated as abstract “mechanical energy dissipation” measured by the quality factor (Q) of the medium. Nevertheless, in physics, no such medium properties exist, and energy dissipation rate represents only one aspect of the process of deformation. For example, compare the four commonly used attenuation measures: the geotechnical damping ratio (x), spectral decay parameter (k) in site characterization studies, and 1/Q and t* in seismology. Of these measures, only x is a true medium property, which is the viscosity of the near-surface mechanical resonator. By contrast, quantities k, 1/Q and t* are parameters of certain types of transfer functions, such as spectral or stress/strain ratios or logarithmic decrements of amplitudes measured in certain experiments. This means that these properties are apparent, and they may (and typically do) depend on boundary conditions, measurement procedures and assumptions. Hypothesizing that such properties (for example, the P- and S-wave, Young’s-modulus, surface-wave, or free-oscillation Qs) are mutually related as predicted by the viscoelastic model is generally incorrect. To overcome these problems, the “attenuation” phenomenon should be approached ab initio, by starting from material properties, differential equations of wave mechanics and the appropriate boundary and initial conditions. Such physical approaches are well known in poro- and thermoelasticity and hydro-mechanics, but they are still poorly utilized in seismology. Several examples of anelastic (but non-Q) forward and inverse physical models of laboratory and field experiments are used to illustrate the above statements.