Many groups have worked on the development of O(N) techniques, from the early nineties up to very recently. Nevertheless, robust O(N) techniques for first-principles MD, where energies can be evaluated with a controlled error, are not yet available. Based on the experience acquired in the literature with O(N) methods implemented using plane waves, wavelets, or other localized basis sets, it appears that methods with controllable accuracy might come from the development of real-space based techniques, which would also require the development of specific pseudopotentials for periodic DFT calculations. 718 (4.6.7) Cancès : What is the error in the output of DFT codes relative to the exact value of a chemical or physical quantity of interest (e.g., the dissociation energy of a molecule, the bulk modulus of a material)? This question is obviously of major importance and is usually addressed by comparing experimental and computational results on large databases. However, such statistical analyses do not really answer legitimate questions of most users, which can be formulated as follows: "What will be the error for the specific system I am interested in if I use this code, with these numerical parameters (basis set / energy cutoff, convergence thresholds, etc.)? How should these parameters be chosen to obtain the accuracy I need, at the lowest computational cost?"