Computational modelling has proven to be a valuable approach in developing theories of spoken-word processing. In this paper, we focus on a particular class of theories in which it is assumed that the spoken-word recognition process consists of two consecutive stages, with an 'abstract' discrete symbolic representation at the interface between the stages. In evaluating computational models, it is important to bring in independent arguments for the cognitive plausibility of the algorithms that are selected to compute the processes in a theory. This paper discusses the relation between behavioural studies, theories, and computational models of spoken-word recognition. We explain how computational models can be assessed in terms of the goodness of fit with the behavioural data and the cognitive plausibility of the algorithms. An in-depth analysis of several models provides insights into how computational modelling has led to improved theories and to a better understanding of the human spoken-word recognition process.