A plasma becomes quantum when the quantum nature of its particles significantly affects its macroscopic properties. To answer the question of when the collective quantum plasma effects are important, a proper description of such effects is necessary.
We consider here the most common methods of description of quantum plasma, along with the related assumptions and applicability limits. In particular, we analyze in detail the hydrodynamic description of quantum plasma, as well as discuss some kinetic features of analytic properties of linear dielectric response function in quantum plasma. We point out the most important, in our view, fundamental problems occurring already in the linear approximation and requiring further investigation. (submitted to Physics-Uspekhi)
