The work in this thesis relates to the transport of salt species in polymer electrolytes, which are solid ionic conductors in which mass transport is similar to that in liquids, rather than in ion-conducting glasses. A brief examination of some of the experimental techniques which have been used to study polymer electrolytes is given before examining in more detail the processes involved when these materials are polarised between non-blocking electrodes. A theoretical treatment is given for various models of polymer electrolytes, in particular polymer electrolytes containing free ions and polymer electrolytes containing free ions and ion-pairs. Non-ideality has been considered for the free ion model. Computer simulations of the free ion and ion-pair model predict that the steady-state current that these materials pass may be proportional to the applied potential difference for many tens of volts, in contrast with the free ion model, where the potential difference limit is of the order of millivolts. The use of the terms "transference number" and "transport number" is discouraged, because of the effect of the motion of uncharged species in practical systems. A new parameter, the current fraction, is defined for steady-state polarisation experiments. An experimental study of amorphous polymer electrolytes is described, in which electrolytes were polarised to steady-state using non-blocking electrodes. The application of the Hittorf technique to these materials has been demonstrated, with true transference numbers determined for some electrolytes. Conductivity and neutron scattering experiments suggest that the reported unusual conductivity behaviour of lithium triflate-based electrolytes does not exist or is not generally displayed.