This special issue contains a selection of papers that were presented at the 24th European Workshop on Computational Geometry (EuroCG'08) held in Nancy, France, on March 18-20, 2008. This workshop is an annual event dedicated to promoting research in Computational Geometry and related fields, within Europe and beyond. Almost 140 participants attended from 19 countries. This issue contains 5 papers that were selected among the 63 contributions presented at the workshop. The original workshop contributions have been expanded into fully developed papers which went through the regular reviewing process before being accepted to this special issue. We thank the authors for their submissions and careful preparation of their manuscript. We are especially grateful to the referees who have provided their time and effort for the benefit of the community. Thanks also to the program committee for their detailed evaluations of the submitted abstracts and for their help selecting the papers for this special issue. Finally, we wish to thank all the authors who submitted their work to the 24th European Workshop on Computational Geometry and contributed to its success.