Quasicrystals can deform plastically at high temperatures by the movement of dislocations like in crystals. Little is known, however, on the mechanisms that control dislocation movements in these structures. In a first part, the crystallography of quasicrystals is introduced as the projection, in the physical space, of a periodic structure in a hyperspace with more than three dimensions (6 in the case of icosahedral structures). The main properties of dislocations are defined in the physical space and in the six-dimensional space. New results are then presented, showing that dislocation movements may have a large component of climb, in contrast with all existing models that are based on glide processes only. Dislocation movements in two-fold and five-fold planes are compared and discussed in connection with macroscopic mechanical properties.