In recent years, x-ray tomography has emerged as a powerful analytical tool in the study of batteries and the processes occurring within. A region of specific interest is the porous electrode and, in particular, the heterogeneous geometry of the porous structure. This thesis introduces the reader to different imaging and physics-based modelling methods used to study the lithium-ion battery. It’s found that none of the image-based models presented in the literature scale well with an increasing number of computational cores. This results in representative elementary volumes being used to approximate the heterogeneity of the porous electrode structure. There is a gap in the literature for the development of a highly parallelisable code that can solve physics equations across large datasets typical of modern tomography. The work presented in this thesis sets out to develop such a code in order to aid understanding of the physical processes within the battery. This thesis also examines the use of x-ray computed tomography to analyse different electrochemical devices, including titanium dioxide electrodes for an aluminium-ion battery, lithium titanate electrodes for a supercapacitor, and lithium iron phosphate electrodes for a lithium-ion battery.