AbstractSimulations of complex systems have seen rapid progress over the last decade not only due to the continuous acceleration of computer resources but also due to improvements of methods and algorithms. Simulations complement experiments and model calculations in the effort to get insight into complex systems such as materials, complex liquids, or complicated molecules. As such, computer simulations are a strongly interdisciplinary field where chemistry meets physics, biology, and material science. Most simulations are based on classical physics because the interaction between atoms or even larger entities can be modeled accurately with classical mechanics for most problems as long as no chemical reactions are involved. If the interaction between atoms in a molecule or between molecules is to be calculated, for instance, to obtain parameters for modeling the interactions in classical simulations, classical physics has to be abandoned because these interactions involve the electron distributions which require a quantum mechanical description. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 388–402 DOI: 10.1002/wcms.40This article is categorized under:Electronic Structure Theory > Ab Initio Electronic Structure Methods