Entropy production is an essential feature of many important kinetic equations and stochastic processes in statistical physics. Maximum entropy and vanishing entropy production can be used to characterise the associated equilibrium. The problem of entropic convergence to equilibrium (in large time) is at the core of kinetic theory. I will start with some classical entropy-entropy production inequalities(for Boltzmann equation or Ornstein-Uhlenbeck process). Then I will discuss the long time behaviour in entropy of the kinetic Fokker-Planck equation (the Langevin diffusion). Partly based on a joint work with Patrick Cattiaux, Arnaud Guillin and Pierre Monmarché.