Order-N first-principles calculations with the conquest code

We summarize the principles underlying the conquest code for first-principles modeling of systems containing many thousands of atoms. Very recent technical developments implemented in the code are outlined. We give illustrations of physical systems currently being studied with the code, ranging from biologically important molecules to Ge hut clusters on Si (001). Our studies of hut clusters require structural relaxation of systems of over 20,000 atoms using electronically self-consistent density-functional theory.