Based on a recent ICFA mini‐workshop held in Oxford, England [1], this paper surveys the computer codes available for simulating the behaviour of charged particle beams under space charge. Modelling tools for both linear and circular accelerating systems are covered. Lists of recent comparisons code v. code and code v. experiment are given and a set of experimental results that might be used to benchmark codes is identified. The Oxford workshop also drew up a detailed spreadsheet of the features of most of the simulation codes in current use, and this is available at [2]. © 2003 American Institute of Physics