Open-cell foams show abnormally large mechanical damping due to the energy dissipated in forcing air in and out of the foam during a deformation cycle. This pneumatic damping has recently been treated theoretically and experimentally. The dependence upon the test-piece dimensions, the frequency of deformation and the viscosity of the fluid has been shown to be in good agreement with the theoretical predictions. The dominant property of the foam structure is its permeability to fluids. This has also been measured for a number of different foams and related to their structural features by means of a simple model. A review is given of these developments.