Dislocations in quasicrystals, as a direct result of the lack of translational symmetry in these materials, possess various salient features. The Burgers vector of a dislocation in an icosahedral quasicrystal is a 6-dimensional vector, which reflects the fact that the dislocation, besides the phonon-type strain field analogous to dislocations in ordinary crystals, is associated inseparably with a further type of defect, the phasons. Phasons are critically involved in the formation and motion of dislocations in quasicrystals and govern the macroscopic plastic behaviour of these materials. In this article the properties of dislocations in icosahedral quasicrystals are comprehensively reviewed, starting from a continuum-mechanical description, via core-structure simulation, to their full experimental characterization. The experimental results presented address the icosahedral phases in the well explored systems Al-Pd-Mn and Zn-Mg-Dy.