Pushing further the analogy that sampling is a (convex) optimization problem on the space of measures, it is natural to ask whether we can accelerate, in the spirit of Nesterov's algorithm for convex optimization. I will introduce the underdamped Langevin diffusion and give an introduction to its accelerated hypocoercive convergence analysis, both in L^2 and also in KL, via Jianfeng Lu's recent Lyapunov analysis based on an optimal transport corrector.