The problems and paradoxes of the Lifshitz theory in application to real dielectric and semiconductor materials are reviewed. It is shown that the inclusion of drift current of conduction electrons into the model of dielectric response results in contradictions with both thermodynamics and experimental data of different experimental groups. Physical reasons why the problems and paradoxes arise are analyzed and found to be connected with the violation of basic applicability condition of the Lifshitz theory, the thermal equilibrium. A recent alternative approach to the resolution of the problems based on the inclusion of screening effects and diffusion current is considered and demonstrated to be thermodynamically and experimentally inconsistent. It is argued that the inclusion of the diffusion current leads to an even deeper violation of thermal equilibrium. Phenomenologically, the Lifshitz theory with role of drift and diffusion currents neglected is shown to be free of problems and in agreement with both thermodynamics and all available experimental data.