We review some of the results obtained for the study of phason, phonon and atomic dynamics in quasicrystals. In the framework of the hydrodynamic theory long-wavelength phason modes are characteristic of quasicrystal and are diffusive modes. Quenched-in phason mode gives rise to a characteristic diffuse scattering, observed in all the ‘stable’ icosahedral quasicrystals studied so far. In the AlPdMn icosahedral phase, above T = 500 °C, equilibrium phason modes are shown to be diffusive modes in agreement with the hydrodynamic theory. The lattice dynamics has been studied by inelastic neutron or X-ray scattering. Well defined acoustic modes are only observed for wavevectors smaller than 0.3 Å⁻¹. Above this value, the mode rapidly broadens as a result of mixing with higher energy modes. We show that the results can be interpreted using the concept of pseudo-Brillouin zone boundary and can qualitatively explain the differences observed in the response function of the ZnSc 1/1 approximant and its quasicrystalline counterpart. The observations are qualitatively and quantitatively reproduced using oscillating pair potentials, which open the route for a detailed analysis of the lattice dynamics at the atomic scale. An exceptional dynamical flexibility is also evidenced in the 1/1 approximant. A brief discussion on the implication of those results on the stabilizing mechanisms of quasicrystals is given at the end of the paper.