During fossilization, the remains of extinct organisms are subjected to taphonomic and diagenetic processes. As a result, fossils show a variety of preservational artefacts, which can range from small breaks and cracks, disarticulation and fragmentation, to the loss and deformation of skeletal structures and other hard parts. Such artefacts can present a considerable problem, as the preserved morphology of fossils often forms the basis for palaeontological research. Phylogenetic and taxonomic studies, inferences on appearance, ecology and behaviour and functional analyses of fossil organisms strongly rely on morphological information. As a consequence, the restoration of fossil morphology is often a necessary prerequisite for further analyses. Facilitated by recent computational advances, virtual reconstruction and restoration techniques offer versatile tools to restore the original morphology of fossils. Different methodological steps and approaches, as well as software are outlined and reviewed here, and advantages and disadvantages are discussed. Although the complexity of the restorative processes can introduce a degree of interpretation, digitally restored fossils can provide useful morphological information and can be used to obtain functional estimates. Additionally, the digital nature of the restored models can open up possibilities for education and outreach and further research.