The words‘fluidization of a non-cohesive granular material by low-frequency vibrations’cover the whole scope of phenomena which are described briefly with the use of precise examples. In most of them, the fluidized medium has a free surface since this condition seems to be required to obtain fluid-like behaviour and convective flows. I also give the example of sand liquefaction which occurs sometimes during seisms for which the existence of a free-boundary condition is not needed. I separate problems linked to the presence of air from those which are induced directly by slight changes in boundary conditions or by the vibrations themselves. If most of the time the convective patterns are produced with vertical vibrations, I demonstrate that other convective patterns are obtained with horizontal vibrations. All these convections occur above an amplitude threshold, which is higher for horizontal vibrations than for vertical vibrations. I demonstrate also that vertical vibrations may stop an hourglass, the physics of which we do not understand. One of the main goals of this paper is to demonstrate that the physics of the sand pile (and then of convection in the sand pile) is mostly governed by friction and dilatancy, which are two nonlinear phenomena; this implies in particular that sand-pile mechanics is quite sensitive to rotations of the principal stress axis, which make these convection patterns quite sensitive to any change in boundary conditions at some stage of vibration, so that their macroscopic behaviour depends on small changes and are quite difficult to predict ab initio, unless the situation is well characterized.