  We describe recent progress in developing practical ab initio methods for
which the computer effort is proportional to the number of atoms: linear
scaling or O(N) methods. It is shown that the locality property of the density
matrix gives a general framework for constructing such methods. We then
describe our scheme, which operates within density functional theory. Efficient
methods for reaching the electronic ground state are summarised, both for
finding the density matrix, and in varying the localised orbitals.
