The physical state of the intergalactic medium can be probed in great detail with the intervening absorption systems seen in quasar spectra. The properties of the hydrogen absorbers depend on many cosmological parameters, such as the matter power spectrum, reionisation history, ionising background and the nature of the dark matter. The spectra also contain metal lines, which can be used to constrain the star formation history and the feedback processes acting in large and small galaxies. Simulations have been instrumental in investigating to what extent these parameters can be unambiguously constrained with current and future data. This paper is meant as an introduction to this subject, and reviews techniques and methods for simulating the intergalactic medium.