We discuss recently discovered problems in the Lifshitz theory of the van der Waals and Casimir forces. It was found that the measurement data of the most precise experiments using metallic test bodies are in agreement with theoretical predictions only under a condition that the relaxation properties of conduction electrons are omitted in computations and the low-frequency behavior of dielectric permittivity is described by the plasma model. Our talk is devoted to similar problems arising for semiconductor and dielectric test bodies. Experiments show that the measurement data are in agreement with theory only if we ignore the influence of free charge carriers which are present in any dielectric material at room temperature. In this connection an experiment is proposed which could demonstrate different Casimir forces between test bodies with almost the same optical properties of the boundary surfaces.

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