Abstract. Science continually contributes new models and rethinks old ones. The way inferences are made is constantly being re-evaluated. The practice and achievements of science are both shaped by this process, so it is important to understand how models and inferences are made. But, despite the relevance of models and inference in scientific practice, these concepts still remain controversial in many respects. The attempt to understand the ways models and inferences are made basically opens two roads. The first one is to produce an analysis of the role that models and inferences play in science. The second one is to produce an analysis of the way models and inferences are constructed, especially in the light of what science tells us about our cognitive abilities. The papers collected in this volume go both ways.Science continually contributes new models and rethinks old ones. The way inferences are made is constantly being re-evaluated. The practice and achievements of science are both shaped by this process, so it is important to understand how models and inferences are made.Despite the relevance of models and inference in scientific practice, these concepts are not only multifaceted but also in some sense their definition, role and purpose still remain controversial in many respects.Let us start with the notion of model. Frigg and Hartmann, for instance, state that: Models can perform two fundamentally different representational functions. On the one hand, a model can be a representation of a selected part of the world (the 'target system'). [...]. On the other hand, a model can represent a theory in the sense that it interprets the laws and axioms of that theory. These two notions are not mutually exclusive as scientific models can be representations in both senses at the same time.