How strict are theoretical bounds for dielectric properties of mixtures?

This report discusses bounds for mixing rules. Several theoretical bounds and limits for the effective permittivity of heterogeneous media have been derived. However, it may happen that the bounds are trespassed in the real-life applications. Examples of such behavior are given for snow, random media simulations, lossy heterogeneous materials, and magnetic and magnetoelectric materials. Reasons for the bound-violation phenomenon are discussed.