The diffusion of ions within a battery material is inherently important to its capacity to charge and discharge electrons through a circuit during its normal operation. Understanding the pathways ions use to diffuse within a crystal structure, identifying where the barrier to movement is small, can inform the direction of future battery research. Two crystalline materials, Na0.8CoO2 and Li0.29La0.57TiO3, have been studied using a combination of experimental and computational techniques due to their promising characteristics. NaxCoO2 is closely related to the commercially dominant LixCoO2 cathode material. They are intercalation materials with rigid CoO2 layers that the Na or Li ions can diffuse between. The effect of ordering of the Na ions within a layer on the diffusion rate has been studied with molecular dynamics simulations by first principles density functional theory calculations using CASTEP. Clustering of ions is observed to enhance the diffusion rate by opening up short range pathways with a greatly reduced energy barrier to diffusion. The diffusion rate of Na0.8CoO2 was measured using quasi-elastic neutron scattering with the signal varying according to the self-correlation function, effectively providing a value for the average time an ion stays in one site between 'hops'. Li0.29La0.57TiO3 is a solid electrolyte with ionic conduction rates equivalent to liquid and polymer based systems. The use of a solid electrolyte has significant advantages, particularly its improved stability and safety. Using single crystal X-ray diffraction, structures of several crystals have been identified, including a completely novel Ruddlesden-Popper structure previously unreported in literature. Quasi-elastic neutron scattering over a large temperature range is used to measure the diffusion rate and activation energy. The hopping geometry is found to be consistent with the predictions of molecular dynamics simulations.