In the collisionless Vlasov theory of excited electrons, plasmas oscillations arise due to their long-range meanfield interaction, and the classical Landau damping concerns decay of such an oscillation. While the damping mechanism is exponentially fast by phase mixing for short-wave perturbations, it's extremely slow or not available for long-wave perturbations (i.e. oscillations may survive and remain as a Klein-Gordon dispersive wave). This talk aims to present recent results on nonlinear Landau damping, focusing on the plasma oscillation regime.