A brief review of two alternative descriptions of non-equilibrium processes in a fully ionized plasma is presented. The example of ‘Landau damping’ is used to demonstrate that some fundamental problems remain unsolved in the kinetic theory of plasmas. These arise from inconsistent descriptions of the transition from the reversible equations of the mechanics of charged particles and fields to the irreversible equations for a continuous medium in the theory of plasmas. These difficulties can be overcome through consistently defining the structure of the continuous medium and the characteristics of dynamic instability of motion of particles. This leads to generalized irreversible kinetic equations that provide the basis for a unified description of non-equilibrium processes in a plasma on kinetic and hydrodynamic scales.