The Geant4-DNA project proposes to develop an open-source simulation software based and fully included in the general-purpose Geant4 Monte Carlo simulation toolkit. The main objective of this software is to simulate biological damages induced by ionising radiation at the cellular and sub-cellular scale. This project was originally initiated by the European Space Agency for the prediction of deleterious effects of radiation that may affect astronauts during future long duration space exploration missions. In this paper, the Geant4-DNA collaboration presents an overview of the whole ongoing project, including its most recent developments already available in the last Geant4 public release (9.3 BETA), as well as an illustration example simulating the direct irradiation of a chromatin fibre. Expected extensions involving several research domains, such as particle physics, chemistry and cellular and molecular biology, within a fully interdiciplinary activity of the Geant4 collaboration are also discussed.