Abstract While some computational models of intelligence test problems were proposed throughout the second half of the XXth century, in the first years of the XXIst century we have seen an increasing number of computer systems being able to score well on particular intelligence test tasks. However, despite this increasing trend there has been no general account of all these works in terms of how they relate to each other and what their real achievements are. In this paper, we provide some insight on these issues by giving a comprehensive account of about thirty computer models, from the 1960s to nowadays, and their relationships, focussing on the range of intelligence test tasks they address, the purpose of the models, how general or specialised these models are, the AI techniques they use in each case, their comparison with human performance, and their evaluation of item difficulty.