In the Vlasov theory of excited electrons, Langmuir's waves or plasma oscillations arise due to the long-range interaction between electrons, leading to the oscillatory behavior of the electric field like a Klein–Gordon's dispersive wave. The classical Landau damping concerns decay of such oscillations, exponentially rapid for short-wave perturbations, however extremely slow or not available in the long-wave regime. This presentation shall provide an overview and the state of the art on this subject.