Carboniferous fossils are often found as three-dimensional voids within siderite (FeCO3) nodules. Traditional techniques of study – splitting the host concretion and inspecting the surfaces revealed – do not allow the investigation of morphology within the part / counterpart, and prevent complete data recovery. X-ray micro-tomography (XMT) and 'virtual palaeontology' can overcome such limitations. This thesis documents the application of XMT to a number of Carboniferous arthropod groups. In the trigonotarbids (Arachnida: Trigonotarbida) the technique has revealed novel features such as coxal endites and tarsal claws, and allowed a taxonomic revision of the family Anthracomartidae. The harvestmen (Arachnida: Opiliones) have a sparse fossil record, resulting from their poorly sclerotized exoskeleton and terrestriality. Two new species have been reconstructed, greatly expanding morphological data from the early history of the group, and the cladistic assignment of both to extant clades supports molecular estimates of early (Palaeozoic) cladogenesis among the Opiliones. XMT of Compsoscorpius buthiformis (Arachnida: Scorpiones) has allowed a taxonomic revision of numerous Carboniferous scorpions, and provided insight regarding the species' mode of life. XMT analysis of stem-dictyopteran Archimylacris eggintoni (Insecta: Neoptera) – now one of the morphologically best known 'roachoid' fossils – has provided evidence that it was a fast runner, an adept climber and a detritivore. Two new species of insect nymph have also been reconstructed: a heavily spined example is quite unlike any previously described taxa, whereas the other has possible roachoid affinities. The investigation of the enigmatic arthropod Camptophyllia has failed to reveal a sternal surface or appendages, but has nevertheless provided new details of the morphology of this unusual taxon. XMT is a powerful new technique for studying siderite-hosted fossils: it reveals their morphology in great detail, and can inform debates regarding the mode of life, phylogeny, and taxonomy of a wide range of Carboniferous arthropods.