This volume contains the edited versions of papers presented at the IUTAM-Symposium Topological design optimization of structures, machines and materials - status and perspectives, held at Rungstedgaard, near Copenhagen, Denmark, in October 2005. The Symposium was attended by scientists in mechanics, optics, and applied mathematics from 19 countries. It is now more than 15 years ago that the so-called homogenization method was proposed as a basis for computational means to optimize the topology and shape of continuum structures. From initially being capable mainly of treating minimum compliance design we now see the basic material distribution idea of the methodology applied to a wide range of structural and mechanical problems as well as to problems that couple structural response to other physical responses. Also, the method has provided insight for micro-mechanical studies, meaning that the method has given feedback to the area which provided impetus to the field of topological design optimization in its creation. Finally, topological design is now an integral part of most FEM software systems and it has become a standard industrial tool in some fields.