We review the basic concepts related with the study of the dynamics of the heavy quarks in the quark-gluon plasma created in ultra-relativistic heavy-ion collisions. We discuss the relevant physical scale as well the difficulties of the present theoretical approaches to self-consistent describe the experimental data at RHIC and LHC.

In the second part, we challenge the assumption of Brownian motion for charm quarks and compare the dynamical evolution of charm and bottom quarks in a Fokker-Planck approach and in a Transport Boltzmann bone. We show that while for bottom the motion appears quite close to a Brownian one, this does not seem to be the case for charms quarks. In particular, larger anisotropic flows are predicted by Boltzmann dynamics toward a better agreement with experimental data at RHIC and LHC.