In this paper, we survey current models of the mapping stage of analogical reasoning. Our description and our critical analysis will be limited to the four models most used and most influential in psychological research : SME, ACMF, IAM and LISA. First, we define mapping, the interest of its study and the constraints generally implemented in the models. Next, we detail the algorithms of the four models with the same example to help the reader to compare these models. Then, we discuss their advantages and their limits. In the last section, we present an epistemological discussion on the problem of stimulus and information coding in the models. We propose some solutions for this problem and suggest a more empirical approach to the study of stimulus encoding.