Modelling cognition in safety needs a balance between psychological soundness and applicability. On the one hand, it requires representing the cognitive processes that are safety relevant. On the other hand, it has to be practical enough to be used in engineering design or safety assessments. The trade-off leads to differences between the models as described in the scientific literature and the way they are practised. However, safety needs a valid approach that covers safety relevant human characteristics as much as possible. The high-level structures of current models in use for safety assessments lack certain human safety issues to a considerable extent. Therefore, the essential aspects of human cognition for safety need to be represented as thoroughly as possible on the high-level structure of a model in order to assure that safety relevant aspects are considered in practice. The genesis will show how these high-level structures were developed, where the current constraints of using models for safety come from, and what the missing aspects are.