The evidence concerning the velocity of glide of dislocations on the (0001) plane of ice Ih is reviewed and related to atomic processes occurring within or near the dislocation core. The velocity is directly proportional to stress at low stress, with a value of the order of 500 Burgers vectors per second at — 18°C and a stress of 105 N m-2. The usual idea of a dislocation core is that it is “crystalline” in the sense that the linkages between molecules are as far as possible the same as those in the normal lattice. For such a model the disorder of protons presents an obstacle to dislocation movement, and recent theories predict that dislocations should not be able to glide as fast as they are observed to do. Various ways of avoiding this difficulty within the context of a crystalline core are discussed, but none seems likely to be successful. An alternative model is that the core is “non-crystalline”, with a disordered arrangement of mobile molecules within it. The movement of such dislocations should not be seriously impeded by proton disorder. Dislocation mobility would then be limited at least in part by anelastic loss due to the stress-induced order of protons in the surrounding lattice.