Mathematical —or mathematico-numerical— models have pervaded all branches of knowledge, and once control theoreticians have become mainly model-builders. Their mathematical skills are called upon to analyze these models, much less to build them. This confers a renewed significance to an epistemological reflection upon what has become the heart of their occupation. We offer some general remarks, and then attempt to reflect on the different epistemological status of (mathematical) models in physics ("the unreasonable effectiveness of mathematics in the natural sciences") and engineering, life sciences, and social sciences, constrained by my limited experience of the second, and very limited experience of the third (except of mathematical finance, hardly a social science).