The subject of this thesis relates to the design of new polymer electrolytes for battery and fuel cell applications. Classical Molecular Dynamics (MD) modelling studies are reported of the nano-structure and the local structure and dynamics for two types of polymer electrolyte host: poly(ethylene oxide) (PEO) for lithium batteries and perfluorosulfonic acid (PFSA) for polymer-based fuel cells. Both polymers have been modified by side-chain substitution, and the effect of this on charge-carrier transport has been investigated. The PEO system contains a 89-343 EO-unit backbone with 3-15 EO-unit side-chains, separated by 5-50 EO backbone units, for LiPF6 salt concentrations corresponding to Li:EO ratios of 1:10 and 1:30; the PFSA systems correspond to commercial Nafion®, Hyflon® (Dow®) and Aciplex® fuel-cell membranes, where the major differences again lie in the side-chain lengths. The PEO mobility is clearly enhanced by the introduction of side-chains, but is decreased on insertion of Li salts; mobilities differ by a factor of 2-3. At the higher Li concentration, many short side-chains (3-5 EO-units) give the highest ion mobility, while the mobility was greatest for side-chain lengths of 7-9 EO units at the lower concentration. A picture emerges of optimal Li+-ion mobility correlating with an optimal number of Li+ ions in the vicinity of mobile polymer segments, yet not involved in significant cross-linkages within the polymer host. Mobility in the PFSA-systems is promoted by higher water content. The influence of different side-chain lengths on local structure was minor, with Hyflon® displaying a somewhat lower degree of phase separation than Nafion®. Furthermore, the velocities of the water molecules and hydronium ions increase steadily from the polymer backbone/water interface towards the centre of the proton-conducting water channels. Because of its shorter side-chain length, the number of hydronium ions in the water channels is ~50% higher in Hyflon® than in Nafion® beyond the sulphonate end-groups; their hydronium-ion velocities are also ~10% higher. MD simulation has thus been shown to be a valuable tool to achieve better understanding of how to promote charge-carrier transport in polymer electrolyte hosts. Side-chains are shown to play a fundamental rôle in promoting local dynamics and influencing the nano-structure of these materials.