The 9th issue of the Transactions on Computational Science journal, edited by Fran ois Anton, is devoted to the subject of Voronoi diagrams in science and engineering. The 9 papers included in the issue constitute extended versions of selected papers from the International Symposium on Voronoi Diagrams, held in Copenhagen, Denmark, June 23-36, 2009. Topics covered include: divide and conquer construction of Voronoi diagrams; new generalized Voronoi diagrams or properties of existing generalized Voronoi diagrams; and applications of Voronoi diagrams and their duals in graph theory, computer graphics, bioinformatics, and spatial process simulation.