In this talk, we survey several kinetic models for plasma dynamics, ultimately focusing on the Vlasov-HMF (Hamiltonian Mean-Field) model. After a brief historical context, we move from the Hamiltonian dynamics of finite N-particle systems to the infinite particle system via the mean field lim. We introduce mathematical tools: Fourier series, linearization, action-angle variables, and the phase-mixing mechanism. These tools reveal how Landau damping, a return to equilibrium in plasma dynamics, emerges at the linear level. Time permitting, I will explain how this linear picture can be extended to a nonlinear stability result (decay for small perturbations) through a bootstrap argument. The emphasis is on building intuition rather than on technical detail, and the talk is designed to be accessible to all PhD students.